MSA MR 2 p.45

 1.  In the equation y=mx+b,  Y is the independent variable which is basically the output, x is the other independent variable which is basically the input, m is the coefficient of x which you could say is the rate at which y goes up by.  And finally, B is the y - intercept which is where the line crosses the y - axis.  

 2a.  You can solve a problem using a graph or table for a linear relationship.  A graph can be used because it shows the relationship between X and Y over a certain amount of time.  It also can give you data about the problem. By using a table you can also see the relationship between x and y.  An example is... Mike is responsible for buying soda for a party, He needs 10 1 liter bottles. He needs to find which store is cheapest for 10 liters.  At store A they sell a 1 liter bottle for $6.00 at store B they sell 1/2 liters bottles for $3.50.  For store A the equation would be C=b6, store B would be C=b3.50 with C= total cost and b=total bottles.  A graph or table come in handy because you are able to see how much it costs for 10 liters of soda for each store.

2b.  Here is an example of a problem that you can solve using. The Problem is Y= 22x+14.  First you want to substitute numbers for variables if possible.  For this question x= 12 so now you can say Y=22(12)+14.  Were trying to find the value of Y so next you want to make sure you do the equation correctly by using correct order of operations.  You want to find 22x12 which is 264.  Now our equation is Y=264+14 so now all thats left is adding so you just do 264+14 which is 278 and that is how you figure out what Y is.

Elizabeth's MSA MR p. 45

1.) y=dependent variable, which is like the output
m=Coefficient of x, which is the rate
x=independent variable, the input
b= y intercept, or the 'head start' or 'upfront charge' the amount you add on
y is the dependent variable, which means that number depends on what x, or the independent variable, is. M is the coefficient of x, which means m is the amount of times it multiplies x by. In other words, you multiply x by m times. B is the y intercept, which is the number you add on, also known an 'upfront price'. So the equation means, the dependent variable (y) equals the independent variable (x) times the coefficient of x (m) plus the y intercept (b). I know this is a linear relationship because you multiply x by the same number every time, and add the same amount on every time (b) and x could be any number, and x effects what y is.

2a.) A table could be used to see a linear relationship because x and y both go up at a steady rate, even if they are not the same rate. X may go up by 1, and y may up by 2, but its still a linear relationship because each point goes up by the same amount each time. To use a graph, look at the line or points, and see if they go up, down, or stay the same in an exact line. Which means no curves, bumps, a sudden increases, decreases, or flat areas.

2b.) To solve an equation, first you write the equation. Then, you rewrite the equation, filling in the numbers you know. Then, if the equation is like y=mx+b and depending on which variable you don't know, you subtract the y intercept (b) from both sides. Then, you divide both sides by m to get the singular version on x. That would be to find out x. To find out y, you would multiply m and x, and then add that to b to get y. For example, y=20, m=5, and b=10.
y=mx+b
20=5x+10
-10 -10
------------
10=5x
\5 \5
------------
2=x
To find out y:
y=mx+b
y=5x2+10
y=10+10
y=20

JACKS MR

1. Y=mx+b means, y=dependent variable,x=dependent variable, m=coefficient of x, which is how many times you multiply x by, and b= the y intercept which is the upfront cost. So i know the equation is sayingthe dependent variable =the coefficient of x times the independent variable + the y intercept.

2a. A table can be used to see if a relationship is linear if the x and y go up at a steady rate. A graph can be used to see if a relationship is linear by seeing if the line goes up without any curves, bumps, changes, etc. then it is linear.

2b. I have used an equation to solve a problem when for example how much it will cost to rent a bike in the city. If the equation was C=15+5n C= total cost

N= number of hours

then I know it will cost me $15 down payment and $5 per hour.

Math Reflection Page 45
1.) Y= dependant variable (output)
M= coefficient of x (rate)
X= independent variable (input)
B= y-intercept (head start)
Y=mx+b is the equation. The y-intercept is the starting rate, or in some problems, it’s the upfront price you pay, or the starting fee, such as in problem 2.3. In that problem, Mighty tee had a start up charge of $49. Then, there was the coefficient, which was n, and for No-Shrink, it was $4.5.
2a.) A table can be used for a linear relationship to solve a problem, by using the numbers. For example: if I wanted to find out how much money someone earned in one week from walking a dog, I would find it in the table as follows:
Days
Money Earned
1
$10
2
$20
3
$30
4
$40
5
$50
6
$60
7
$70
8
$80
9
$90
10
$100
You would find where the table says 7 days (which is one week), then see how much money was earned, which in this case is $70.
A graph can be used to solve a linear relationship in a problem, by using the x and y axes. For example:
X
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
9
8
7
6
5
4
3
2
1
0
You start with the x axis, then find where the line lines up with a number from the y axis, and find where the numbers meet on the line, to get your coordinates.
2b.) I have used an equation to solve a problem, by substituting the variable, with what ever number you are using. I used an equation in problem 2.3, where when I wanted to find out how much 100 shirts cost; I replace the variable with 100. 49+n, then I replaced n with 100, 40+100=$149. That’s how I used equation to solve a problem.

MSA Reflection p.45

1.)A linear relationship that is represented by the equation, y=mx+b. In this equation, the y is the dependent variable or the out put. An example is on a graph, it would be the distance. The m is the coefficient of x. In other words, this is the rate. The x in this equation is the independent variable, or the input. On a graph, this would be known as the time. and finally the b. The b is the y intercept. For an example, the y intercept is like in a race, someone gets a head start. Or if there is like a problem with a price that moves at a constant rate. The y intercept would be like if you pay first a little price to start off then move at a constant rate.

2a.)For a table, you can use it to solve a problem by seeing all the numbers that go up a constant rate and then put them in the problem you are trying to solve. Then for a graph you can see on the graph, the way it is plotted how it moves up. Then you can just read how it moves up then put what you see in the problem.

2b.) I have used an equation to solve a problem by putting the numbers needed in the equation, substituting the variables and then just simply solving the equation. Or if i am making up my own equation to show other people how to solve then i would simply do the work I did Backwards to find the equation that I am looking for.

Page 45 Math Reflection

1. An equation like the one y=mx+b has a dependant variable, an independant variable, a y intercept and a coefficient of x. Y in the equation is the dependant variable or the output in a table. X is the independant variable or the input. B is the y intercept or on a graph the point where the line intercepts with the y axis. M is the coefficient of x or the rate.

2. a. Say the linear relationship was y=3x and you needed to find out what y would be if x equaled 5. In a table you would look in the x colum until you got dwon to 5 then you would look at the number next to it in the y colum which in this case would be 15. So the answer to your problem would be 15=3*5 or just 15. On a graph if you were using the same relationship and you wanted to find the same thing you would look at the x axis until you found 5 then you would look at the line and move your finger toward the y axis adn the number would be 15.

b. In an equation you would substitue the numbers in for the variables. Like in the equation x=4y and y equaled 2. the equation would then be x=4*2 and 4 times 2 is 8 so x would equal 8.

Math Reflection p. 45

1. An equation of the form y=mx+b has two variables (x and y), a y-intercept (b), and a coefficient of x (m). A y-intercept is the point where the line crosses the y axis or on a table when x is at 0. A coefficient of x is the number that multiplies x. For example, in the equation y=5x+20, 5 is the coefficient and 20 is the y-intercept.

2. a. A table can be used to solve a problem for a linear relationship. If you have what x equals you look at that number under x in the table, and next to it will show you what y equals, or vise versa. A graph can be used to solve a problem for a linear relationship. If you have what y equals, you look at that number on the y axis, then go to the right until you reach the line and look down from that point to find x, and vise versa.

b. To use an equation to solve a problem first write the equation. Then fill in the variables you know.If the equation is set up like y=mx+b, and you know the y, next you would subtract the y-intercept (b) from each side. Then divide each side by he coefficient (m) and you will end up with your answer. For example if y= 40:

y=5x+20
40=5x+20
-20 -20
20=5x
/5 /5
4=x

If you know x, you would simply solve the equation. For example if x=8:

y=5x+20
y=5(8)+20
y=40+20
y=60

MSA MR 2

1) What I know about a linear relationship represented by the equation of the form y= mx+b is that y is the dependent variable. It depends on the independent variable. In this equation, the independent variable is x. m is the coefficient of x. Coefficient is the number that multiplies a variable in an equation. m is usually the rate. In Emile and Henri's problem, Emile's rate was 2.5 miles per second. b is the y intercept. y intercept is the point where the line crosses the y axis on a graph. For example, in Emile and Henri's problem, Henri got a 45 meter head start. When the x axis was at 0 seconds, Henri was already at 45 meters.

2a) If you have a table or a graph, that means you have an equation. Therefore, when trying to find an x or y value that corresponds to the equation in the problem, a graph or table can help you locate the point that you want to find in the linear function. This point will represent an x or y value.

2b) I have used an equation to solve a problem by plugging in numbers for the variables. For example, if I wanted to buy 15 shirts and the cost per shirt was $8, the equation for this would be:
C= 8n
C= cost
n= number of shirts.
To see what the cost would be for 15 shirts, I would plug in 15 instead of n. Then I would solve the equation. 15*8=120. The cost for 15 shirts would be $120.

MR pg. 45

By: Jonah Ogburn

1.) What I know about linear relationship is that in the equation y=mx+b is that b is the y intercept, that is the number or amount you begin with on the y axis when the x axis is at zero. I also understand that m is the coefficient in the equation which means its the rate at which the equation goes up on the x axis. The x Stands for the independent variable, it can also be considered the input in an input-output table. The y stands for the dependent variable, or in the case of an input and output table the output.

2.

a.When using a table to solve a linear equation you can use the organized numbers to see how the equation works.When using a graph to solve a linear equation the relationship can be solved easily by having all the information plotted on the graph and to see how the rate goes up, graphs usually show all the information in a problem. .

b. I have used an equation to solve a problem by plugging in the number of shirts and the number of hours(or any other unit of time). Next I used the equation I just created to solve the equations cost. Say the cost per shirt was 10 dollars then i find out how many shirts were bought, lets say 6. Then i plug in my numbers to the equation.

equation:c=$10n c= total cost n= number of shirts

Finally I would check my answer by working my way backwards if c equaled 60, I would divide 60 by 6 to get my answer 10.

MSA MR2

Duncan Dietz
6/6/10
Red Rectangles

MSA MR2

1. Y =mx+b is an equation for Y. In this equation Y is the dependent variable that is being solved for. X is the dependent variable. X times something usually equals Y . The number that is multiplied by X is always known as M or the coefficient. B is the Y intercept or when X is 0 Y is at that number whether B is 0 or 200.

2.a. A graph can be used because it shows how data and the relationship between X and Y altar over a span of time it just uses a line.. To solve a problem with a linear graph you first make sure the line is long enough. Then read the equation. I will use Y=3*X=0. In this equation we are solving for Y. So when X=4 what is Y. First you make the line. Next find where the X axis is 4 then go up to the line and then horizontal where the line meets both the X and Y axis. In this case it would be 12.

Tables show the exact same thing just in a different way, it using columns and not lines. Now, to use a table you must first make a table. Then in the X column find where it is 3 (I am using the same equation as before). Then look in the adjacent cell in the Y column. The number in the column should be 12.

2.b. Time to solve this problem with an equation. In the problem Y=5X+3 I must find Y.
So if X is 7 what is Y? First substitute numbers for variables if possible. Y=5*7+3. Then do order of ops. Y=35+3. Finally add the 3. 35+3=38 so Y=38. But, if I know Y and need to find X the equation is much different. Y=43 43=5X=3. First, subtract like terms. 43-3=5X=3-3 or 40=5X. Then, divide each side by 5 (side with the variable). 40/5=5X/5 so 8=X.

MSA Math Reflections p.45

1. A linear relationship represented by y=mx+b shows the relationship for the y-intercept in an equation, the point where the data line crosses the y-axis on a graph. In this equation, y depends on the x. b represents the point where the line crosses the y-axis, or when x=0. m represents the coefficient, or the number that a variable is multiplied by in an equation, so mx actually means m*x.

2a. A table or a graph for a linear relationship can be used to solve a problem because it shows you how the data changes over time. For example, if the student council were to purchase field day tee-shirts, they may check the prices of Store A and Store B. Store A charges $4.50 a shirt while Store B charges an initial down payment of $50 but only charges $1.50 a shirt. The table or a graph would be helpful because it would show how many shirts you would need to buy before the price is equal and how much is charged for that price. So instead of just looking at an equation, you would actually see how the data changes over time.

2b. One problem that I used an equation to solve was the problem with Fabian's bakery. The problem was "What are Fabian's monthly expenses and his monthly income for January if he sells 100 cakes that month?" There were two equations, one for the expenses and the other for income. The expense equation was E=825+3.25n, E represents the monthly expenses and n represents the number of cakes sold that month. The income equation was I=8.25n, with I representing the monthly income and n representing the number of cakes sold that month. To find the expenses and income, all that I needed to do was replace the n variable with 100 to stand for the 100 cakes sold, and the equation allowed me to find the month's expenses, $1,150, and the month's income, $820.

MSA MR2

1. The equation y=mx+b is linear this is because that y always x is always increased by the same number. and although you add b it does nothing exept increase the begining number by what ever it is because you add it after the multiplacation.

2.a. A graph would prove a equation lineir and tell you how much to increase each time. However a table tells you the anser but only to some extent because the graph could not go on for ever.

b. A equation is quite simple to solve, it is just like a math problem but with a variable. Like if m=7 x=4 and b=3 than it would be a problem like y=7*4+3 than y would equal 32.

MSA MR 2

Ryan Jonuskis

MR 2 MSA Pg. 45

1.) Y equals the final answer, M equals the rate or coefficient, X equals the starting price, number, etc., and B equals the Y-Intercept.

2.)A.) A table or graph can be followed nil the final answer is found because it increases by a steady rate.

B.) I have used equations to solve problems usually by finding the value of X in the equation. If not I usually have to use the equation backwards.

Math Reflection 2

By Krystle T

1.) What I know about linear relationship is that in the equation y=mx+b is that b is the y intercept which is what you start with on the y axis when on the x axis it's zero. I also know that m is the coefficient of x, which is also known as the rate. This is usually the cost per some type of time, or measurement per some type of time. The x Stands for the independent variable, or the input in an input-output table. They stands for the dependant variable, or the output in the input-output table.
2.)
a.) A table for a linear relationship can be used to solve a problem by the data given and the numbers organised together. A graph for a linear relationship can be used to solve a problem by having the information put on a graph showing the rate the information goes at, and it shows most of the information for the problem.

b.) I have used an equation to solve a problem by plugging in the number of shirts, or number of hours, minutes, and seconds. Then I use the equation to figure out how much that was. If it doesn't ask a cost or something, and ask for how many hours, seconds, or minutes it was for lets say $5 then you would do the equation backwards. For example if the equation was
c=cost
n= number of shirts
equation:
c=$5n
I would work my way backwards if c equaled 30, I would divide 30 by 5 instead of multiplying them to get my answer, 6.

MSA MR 2

1. A linnear relationship is a relationship that goes up at a constant rate. Variable M is the coefficient in the problem. The coefficient is the number in an equation that multiplys the variable. Variable b is the y-intercept. This equation would be a linnear relationship. It is multiplied by the same number each time and goes up steadily.
2.a. A table or graph for a linnear relationship can be used to solve a problem because it shows all the information needed for the problem. The graph will show where the line goes up with the numbers. The table will show all the numbers and data organized.
b. I used an equation to solve a problem by putting the numbers in the equation and doing each part step by step. for example, when i needed to figure out an amount of money someone made babysitting for a certain amount of hours.

Troy Burditt's MR

1. A linear relationship is an equation that goes up at a steady rate. In the equation y=mx+b each variable stands for a different thing. The variable m is the coefficient which is the number that multiplies the a variable. The variable b is the y-intercept which is where the line crosses the y-axis. Finally, the variable x is the independent variable or in put and the y variable is the dependant variable or out put.

2.
a. For a graph that is linear you can solve a problem by finding where the line lines up with the x and y axis. Also for the table it could be like an in and out table.

b. I have used an equation to solve a problem like if two phone company's are a plan you could use an equation to figure out which one is more expensive to sign up for and have for a year.

Yesterday in class, we worked on equations. We learned how to find out what the variable in the equation was by adding and taking away numbers on both sides. An example of a problem that we did was 7+3x=5x+13. To find out what x is, you have to get x on one side, and the other numbers on the other side.
7+3x=5x+13
-3x -3x Take away 3x on each side to get x on the right side of the = sign.
7=2x+13 This comes out to 7 on one side, and 2x +13 on the other. We have x on one side now, but in order to figure out what it is, you have to take away the 13 on the right side. And whatever you do to one side, you have to do to the other.
7=2x+13 To get the x alone, you have to take away 13.
-13 -13
-6=2x To find out what x is, always divide the number on the side without the x by the number with the x. -6/2= -3. x= -3

Now, you have to check your answer. You do this by inserting the answer that you got for x into the equation wherever you see x.
7+3(-3)=5(-3)+13
-3(-3) -3(-3)
7=2(-3)+13
-13 -13
-6=2(-3)
2*(-3)= -6
X=-3

Moving Straight Ahead Problem 3.3 hw launch 3.4

Moving Straight Ahead Problem 3.3 hw launch 3.4

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Moving Straight Ahead Problem 3.3 rr

3.3 rrMoving Straight Ahead Problem 3.3 rr

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Today in class, we focused on maintaining equality. That means keeping the numbers that you are working on balanced. For example: 85=70+15. If you add 5 to 85, then you have to maintain equality by adding 5 to 70+5, and the numbers will stay equal.
We also worked on problem 3.2, which was about coins and pouches. What we had to do was keep the number of coins per pouch equal, which was maintaining equality. If there were 3 pouches and 2 coins on one side, then you would cross out 3 pouches and 2 coins on the other side too, to keep the number of coins per pouch equal. That is what we worked on today in math class.

Moving Straight Ahead Problem 3.2

Moving Straight Ahead Problem 3.2

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Math Relfection p. 23

1. The dependent variable changes at steady rate, as the independent also changes at a steady rate. For example, the independent variable may go up at 1, and the dependant variable may go up by 3. Also the dependent variable may go down by steady rate also, like the independent variable goes up by 1, and the dependent variable goes down by 5.

2. A pattern for a linear relationship shows up in a graph through a straight line. It could be any straight line, horizontal, vertical, or diagonal. As long as its a straight line, its a linear relationship. A linear relationship shows up i a table by the numbers increasing, decreasing, or staying the same in a steady rate. Like, x starts at 1, y starts at 2. Then, as x increases by 1, y stays the same. A linear relationship is shown in a equation by as x increases or decreases, y increases or decreases by a steady rate, not jumping around to random numbers.

1. As the independent variable increases at a steady rate so does the dependent variable. For example if x increases by 1 and does that the entire time and y increases by 3 and does that every time then the relationship is linear. So if i was to raise money for a bike ride and I got $100 no matter how far i rode. Therefore the relationship is linear because it does nothing at a steady rate. However if I was a shopper and I had $100 to start and spent $10 per week for 10 weeks then the relationship is linear because it decreases at a steady rate.
2. A relationship shows up in a graph, a table, and an equation. It shows up in a graph because if the line is straight then the relationship is linear. It shows up in a table because you can see the numbers increasing at a steady rate. It shows up in the equation because you can see how the x and y increase.

Math Reflection

1. In a linear relationship the dependent variable (the y axis on a graph) changes along with the independent variable (the x axis) but not at the same rate usually. If Steve is selling T-shirts at a concert for $3.00 per T-shirt you could make a table that looked like this..

X Y

1 3

2 6

3 9

4 12

5 15

6 18

7 21

8 24

9 27

10 30

As X (the independent variable) increases by one Y (the dependent variable) goes up by 3. If you put it in an equation it would be X * 3 = Y.

2. In a linear relationship the pattern of change can show up in a graph, table and an equation. In a graph you can tell if it's linear because the graph will be in a straight line and always is going at the same rate. An example of this is Steve selling his T-shirts since he has a linear equation it automatically makes him have a linear graph. You can tell if a tables linear because the numbers in the table increase or decrease in a steady rate. For example in Steve's table for every T-shirt he sells he makes $3.00 and as the table goes on Steve's money increases by a steady rate of $3.00. If you look at an equation you tell its linear because all of the numbers are compatible with each other and don't increase and decrease in the same graph or table. An example of this would be for each T-shirt Steve sells he makes $3.00 and to get how much money he makes for selling X amount of T-shirts you would do X * 3 = Y. X being the number of T-shirts bought and Y being the total money he makes off selling them.

MSR Math Reflection 1

1.  In a linear relationship, as the indipendent variable changes, the dependent variable can change as well.  Since it is linear, the independent variable changes by a steady rate while a dependent variable does as well.  An example is that as the independent variable increases by 1, the dependent variable incrreases by 5.  They will both always increase or decrease at the same rate. 

 

2.  The pattern of change in a linear relationship shows up in a table by X increasing or decreasing by the same number every-time and then Y increasing or decreasing by the same number everytime.  It shows up in a graph because the line will be a straight line.  You will be able to see that every data point incereases or decreases on the X axis by a consistent rate while the the data point increases or decreases by another number every-time on the Y axis.  It shows up in an equation because it will say Y equals a certain number times X which shows that it will alwyas be a steady rate.

Math Reflection

1. In a linear relationship the dependent variable changes as the independent variable changes, but they often don't change at the same rate. A linear relationship is one that changes at a constant rate and shows up as a straight line when graphed. The dependent variable is the one that depends on the other variable, and is the y that belongs on the y axis. The independent variable is the one that keeps going no matter what. It is the x that belongs on the x axis. The independent variable often goes up by 1. As the x goes up by 1, y goes up at a constant rate as well. An example of this in an equation is: y=5x or y=x+3 or y=7 (which would create a horizontal line on a graph), or y=60-5x (a decreasing linear relationship).

2. The pattern of change (or rate) in a linear relationship shows up in the table, graph, and the equation. The rate shows up in the table in the numbers. The x variable often increases by 1 and the rate will be in the numbers, which often takes some searching to find. You must look at the relationship between the y and x variable to find the pattern of change. You can tell whether the linear relationship is increasing, decreasing or not changing by observing the y or dependent variable. The pattern of change shows up in the graph on the line. As the x is steadily increasing, the y will be changing at a constant rate, and that is where the rate is to be found. In an equation, the rate is found in the numbers surrounding the y and x variables. The rate can be found in the equations above. In the equation y=5x, the rate is 5 times the independent variable. In the equation y=x+3, the rate is 1 plus a constant of 3.

Math Reflections MSA 1

1. As the independent variable increases or decreases so does the dependant variable. For example if an equation was Y=3X than every time X increases by 1 the Y increases by 3. Or if it was M=50-2W than every time W increases by 1 M decreases by 2.

2. In a graph you can tell if it’s linear if the line is straight. In table you can tell if it’s linear if the independent variable and the dependent variable both go up at a constant rate. In an equation you can tell if it’s linear if the equation has an independent variable a dependant variable and a rate.

MSA Mathematical Reflection 1

1. The dependent variable changes as the independent variable changes in a linear relationship by having the x variable ( independent variable) increase or decrease, the y variable (dependent variable) increases or decreases too. For example if a person named Kate buys two kittens every week she would have more kittens increasing by two every week that goes by.

Kate's Kittens
X Y
0 0
1 2
2 4
3 6
4 8
5 10

2. The pattern of change for a linear relationship shows up in a table, a graph, and an equation. The pattern of change for a linear relationship shows up in a table by having a repeated pattern increasing or decreasing at a constant rate. For example if the rate for Kate and her kittens is 2 kittens per week, then her table shown in number one would have the weeks(x) go up by one, and the kittens(y) go up by two's. The pattern of change for a linear relationship shows up in a graph by having the graph plots from the table go in a straight line. The line can go either way, in a straight line going up in a diagonal, in a straight line going down in a diagonal line, and or sideways in a straight line, parallel to the x axis. For example since Kate and her kittens is linear, then on a graph for every week two would go up in a diagnol by two on the y axis ( # of kittens), and would go in a straight line. The pattern of change for linear relationship shows up in an equation by having the equation work for all the numers in a constant rate. An example is also using Kates kittens by having the equation be, y=x2. These are some things to look for a linear relationship in tables, graphs, and equations.

1) In a linear relationship, the dependent variable changes as the independent variable changes. As the x variable (independent variable) increases or decreases, so does the y variable. That is a linear relationship. Example- This is a linear relationship because as x increases by 1, y increases by 2. They both increase at a steady rate, which makes it linear.
x y
0 0
1 2
2 4
3 6
4 8
5 10

2) The pattern of change for a linear relationship shows up in a table, a graph, and an equation.
Table- The pattern shows up when y goes up or down at a constant rate while x does also.
Graph- The pattern shows up when the line is straight.
Equation- The pattern shows up in an equation when the equation works for all numbers and they come out in a constant rate.

MSA Math Reflections 1

1. How the dependent variable in a linear relationship changes depends on how the independent variable changes. For example, if in the bike-athon, Mr. Murphy's class generated $200.00 to give to charity. Each week they donate $20.00 to the local Children's hospital. The independent variable is weeks and the dependent variable is the money left in the account. As the weeks increase by one, $20 is deducted from the class account. Another example of this is Joey works for his neighbor. For every hour that he works, he gets paid $10.75. The independent variable is hours while the dependent variable is how much Joey gets paid. As the hours increase by one, Joey earns $10.75 more.

2. The pattern of change in a linear relationship shows up as:

Graph, A straight line going either up or down.

Table, Increases or decreases with the same rate as time moves on.

Equation, A steady rate, if the same amount is added or taken away as time moves on.

1. The dependant variable changes as the independent variable changes in a linear relationship, because if the independent variable increases, so does the dependant variable, and if the independent variable decreases, so does the dependant variable. For example, in problem 4 on page 13, as the time increases by 1 hour, the distance increases by 6.5 miles.

2. The pattern of change for linear relationship shows up in a table, because if there is a steady increase in the numbers, then there will be a linear relationship, but if the numbers have no pattern, there will not be a linear relationship. The pattern of change shows up in a graph, because if there is a straight line on the graph, that shows a linear relationship between the numbers, and if the data in the graph doesn't make a straight line, then there will not be a linear relationship. The pattern of change for linear relationships show up in an equation, because if the equation does not work for all numbers, then there will not be a linear relationship. If the equation woks for every number that you try and it makes a linear relationship, then the equation and data are linear.

Math Reflection

1. The dependent variable changes as the independent variable changes in a linear relationship. If the independent variable increases by 1, and the dependent increases by 5 each time, it is changing in a linear relationship. It is changing in a linear relationship because it is going up by 5 each time, and it doesn't change. If you sketched a graph the line would come out straight because it is evenly going up by 5 each everytime the independent variable increases by 1. For example, if the independent variable increases by 2 each time, and the dependent variable is increasing by 4 each time, it is changing in a linear relationship.

2. The pattern of change for a linear relationship shows up in a table, graph, and an equation of the relationship. It shows up in a table, if X shows up as 2,4,6,8,10 and Y shows up as 10,20,30,40,50, then it is linear because it is increasing by the same number (10) every time it increases by 2. In a graph a pattern of change in a linear relationship would show up by showing a straight line on the graph. For example, if X was increasing by 5 on the X axis, and Y was increasing by 20 on the Y axis, then a straight line would come out when you graphed it. The pattern of change for a linear relationship shows up in a equation of the relationship because the equation stays the same with the same numbers. For example, if X was 1 and Y was 5 the equation would stay as 5y=x.

MSA Math Reflection 1

1. As the independent variable changes, the dependent variable does too. It either increases, decreases, or stays the same. For example, if the independent variable is weeks and the dependent variable is money, the dependent variable will increase if you receive money, decrease if you spend it, or stay the same if you don't spend or get any.
2. You can see patterns and linear relationships in tables, graphs, and equations. In a table, you can see the relationship if the data increases at a steady rate. For example, if money increases by $5 every week. In a graph, you can see the relationship if there is a straight line of data points, increasing, decreasing, or staying the same at a constant rate. In an equation, there must be a number that can be multiplied, divided, added, or subtracted by the independent variable to equal the dependent variable. For example; m=5w. M= amount of money W=weeks. There are many ways to figure out if there is a linear relationship of data.

Math reflection

1. If the graph is linear than the dependent variable goes down at a steady rate. So as the independent variable goes up or down the dependent variable will go up or down by the same number every time. For example on p. 11 problem 1.4 part B has a graph that is linear because the dependent variable goes down by 10 every time the independent goes up by 1.

2. Graph: If the line is a straight line than it is a linear relationship. Table: If it is miles per hour the miles should go up or down at a steady rate as the hours go up than it is a linear relationship. Equation: If the equation is like y=x with an exponent over the x it is not linear but if the equation is like y=2x+73 it is linear. Or even if it is like y=53 it is linear.

1) A dependent variable changes as the independent variable
changes in a linear relationship when a number or a unit is
changed and the line that will be put on the graph when it is
graphed will not be straight it will have bumps.

2) The pattern of change shows up on the graph wjen the line
isnt straight, it shows up on the table when the pattern of
numbers suddenly change from going up by a certain ammount
and changes to going up by a different ammount that the other
numbers are not and the pattern shows up in the equation when
the equation doesnt work for a certain number.

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Moving Straight Ahead

Today in math class, we did some more with linear relationship. First we did a do now that consisted of two tables and we had to figure out if they were linear. We were asked to look at both tables and find out which ones were linear. To find these out we needed to know if these were a straight line on a graph because if it is, then we know that it is linear relationship. We could have found out if it was linear by seeing if the table did not change, but that it was consistent. This brings me to my other description on what we learned to day. We learned what a steady rate is and how and where to use them. For example in one of the boxes, there was a five in one column and a 18 in the one next to it. This graph was linear because as each went up if you multiplied it by five column then used the steady rate which is 3. So 5x5+3= 18. the next two numbers were 10 and 33. So 10x5+3=33.

-Dan

Moving Straight Ahead Problem 1.4

Moving Straight Ahea Problem 1.4 wrap up rr

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Moving Straight Ahead Problem 1.4 hw

Moving Straight Ahead Problem 1.4 hw rr

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Friday in class we learned about different types of linear relationships. When I say this I mean that we learned about decreasing and non - moving linear relationships.
For example one of the problems we did in class was problem 1.4. One part of the problem told us to make a graph of the class who took $12 out each week to buy books. The graph decreased by 12 each week and because it is a steady rate it qualifies as linear. Another problem we did was for homework. The problem was to graph 3 people who were raising money for a walkathon. One of the kids was earning $10 no matter how far she walked so her graph was a straight line from 0 meters to x meters. Since her graph steadly doesn't go anywhere it is linear. In short if the rate is steady the relationship is linear.

More Fractions, Percents & Proportions

Pre-Algrebra 6 5 & 6 6a

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Fractions, Percents & Proportions

Pre-Algrebra 6 2 Proportions Rr

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Percents

On Friday in math class we worked on percents into decimals, percents into fractions, decimals into percents, and percents into mixed numbers too. Somethings we did to practice were problems like write 30% as a fraction in simplest form which would be 3/10. Another problem would be for us to figure out what 6.35% would be in decimal form. The answer would be 0.0635. The way to figure this out is 6.35 divided by 100 which would eaqual on a calculator 0.0635. Or an easier way of doing this is to move the decimal point in 6.35 over backwards two spaces because its divide by 100. We did many prolems like the ones shown in this paragraph. some where confusing like the problem with 6.35% into a decimal. This is what we did on Friday in class.

Krystle T.

Thursday, March 11th

Today in math class we worked more with proportions. In our groups, we completed problem 4.3. To solve proportions, all you have to do is make equivalent fractions. For example, to solve the enchiladas problem you would make two fractions, 3/705=240/x. Then all you need to do is find the variable, x. To find it, you figure out what makes the equation true. We did 240/3=80, and then 705x80= 56,400 calories. Then they make equivalent fractions.

Comparing & Scaling Problem 4.3

Comparing & Scaling Problem 4 3 Rr

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Today in Math class we worked on problem 4.2 in Comparing and Scaling. This problem involved applications for proportions. An example of this is "Jogging 5 miles burns about 500 calories. How many miles will Tanisha need to jog to burn off the 1,200-Calorie lunch she ate?" We also had to come up with a proportion for every problem we solved. A proportion for this problem is 5/x miles=500/1,200 calories, X=12. In this proportion, x was how many miles Tanisha would need to run in order to burn the calories. This proportion shows the relationship between calories burned, and miles run. It shows that the relation ship is that about 100 times as much calories are burned than the miles run, in the problem it was 5 miles burns 500 calories.

Comparing & Scaling Problem 4.1 Intro

Comparing & Scaling Problem 4 1 Intro Rr

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Math Class March 2 2010

Today in math we worked in groups on the Math Reflections. The problems compared peppers and their prices. We had to find the unit rates. To find the price per pepper you would divide $1.50 by 3. To find how many peppers per dollar you would divide 3 by $1.50. We also had to make an equation to show the price for a number of peppers. N*.50=P

Comparing & Scaling Problem 3.4

Comparing & Scaling Problem 3 4 Summary

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Math Class, Wednesday February 24

In math class we wrapped up problem 3.2 and started problem 3.3. In problem 3.2 we had to find Sascha's rates in miles per hour for each part of her trip. We had to figure out which part she went the fastest, and the slowest. Also you had to figure out how long it would take you to travel as far as she did in the same amount of time going 13 mph, and the last thing we had to solve was the steady rate we would have to mantain to keep up with him, and tie him. In problem 3.3 we had to compare CD prices between two different stores. We had to find out which store had a better price for each CD. We had to figure out an equation that you could use to calculate the cost for any purchase of CDs. Then, the next problem we had to solve was using the equation to write new ones including 5% tax on any purchase. On the next problem we had to figure out an equation of the cost of any order for discs on a website that cost $8.99 each with no tax, but 5$ shipping on any order. The last problem we solved was answering "How many discs do you have to order from the website to get a better deal tha buying from Music City?" and "How many discs do you have to order from the website to get a better deal than buying from CD World?". In class we also learned about rounding. We learned 5 and up, you round to the next number, but anything under 5 you keep the number the same. We learned more about rates in wrapping up 3.2, and we learned more about solving problems with tax in completing 3.3.

Comparing & Scaling Problem 3.4 Introduction

Comparing & Scaling Problem 3 4 Intro Rr

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Comparing & Scaling Problem 3.3

Comparing and Scaling Problem 3 3 Rr

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Math Class on February 23, 2010

In class today we worked on problem 3.2 on page 35 in groups. It shows at the top of the page how far Sascha traveled by bike after certain amounts of time. He stopped 3 times to record his time and distance. By stop 1 he had gone 5 miles in 20 minutes. 5/20 =15/60, which means 15 miles in 60 minutes, or 1 hour. This means he went 15 MPH for the first portion of the ride. By the second stop he had went 8 miles in 24 minutes. 8/24= 1/3= 20/60. That means 20 miles in 60 minutes, or 20 MPH. For the last one he went 15 miles in 40 minutes. 15/40= 22.5/60. That means 22.5 miles in 60 minutes, or 22.5 MPH. It is also okay to put the minutes as the numerator and the miles as the denominator. As you can tell, Sascha traveled the fastest at the third stop, and slowest at the first stop. If you were going 13 MPH on a bike it would take you 2 hours and 9 minutes to travel as far as Sascha did. Sascha traveled 28 miles (15+5+8). Our group decided to figure out how long it would take us to travel 1 mile going 13 MPH. 60/13=4.6. Since this is how long it would take us to travel 1 mile, we then multiply 4.6 by 28. 4.6*28=129.23. Then we divided that by 60 and got 2.15. The .15 represents 15/100 which equals 6/60, or 2 hours and 9 minutes. To find Sascha's steady rate, you find his average speed by adding 15+20+ 22.5=57.5. Divide this by 3 to find the average speed.

Comparing & Scaling Problem 3.2 wrap up

Comparing & Scaling Problem 33.2 wrap up rr

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Comparing & Scaling Problem 3.2 Introduction

Comparing & Scaling Problem 3.2 Rr

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Comparing & Scaling Problem 3.1

Comparing & Scaling Problem 3 1 Rr

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Yesterday in math class we did the orange juice problem. In this unit we have been using fractions, ratios, differences, and percents and these played a big part in this problem.
One thing we had to do in the problem is found out how many bathches we would need to make for 240 campers if each camper got 1/2 glass. For one off the problems there were 2 cups of concentrate and 3 cups of water and we found that to make 120 cups we would need t make 24 batches. We found this by doing 2 and 3 makes 5 and 5x24 =120. Another thing we had to do with this problem is if the ratio is 5 (cups of concentrate) to 9 (cups of water) and we need to find what fraction of the mix is water it would be 9/14 not 9/5. For mix A to find the cups of water and concentrate you multiply 2 (concentrate) by 24 which equals 48. Then you multiply 3 (water) by 24 again and get 72. This just scratches the surface of this problem and hopefully it helped.

Comparing & Scaling Problem 2.1 - The Orange Juice Problem

Comparing & Scaling 2 1 Rr

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Comparing & Scaling Problem 1.3

C&S 1 3 Rr

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Comparing & Scaling Problem 1.2

C&S 1 2 & 1 3 Part 1 Rr

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Comparing & Scaling Problem 1.1

1 1 + 1 2 Intro Rr

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Daily Scribe

Today in math class, we started a new unit about comparing and scaling. It's all about comparing ratios, data, and the size of objects. The problem we worked on today was about comparing which soft drink people like better: Bolda Cola and Cola Nola. In this case, people preferred Bolda Cola over Cola Nola. It gave us soma data that a group of people found. The data included: 1.) In a taste test, people preferred Bolda Cola outnumbered those who preferred Cola Nola by a ratio of 17,139 to 11,426. 2.) In a taste test, 5,713 more people preferred Bolda Cola. 3.) In a taste test, 60% of the people preferred Bolda Cola. 4.) In a taste test, people who preferred Bolda Cola outnumbered those who preferred Cola Nola by a ratio of 3 to 2.
It asked which one could be used to best promote their business of Bolda Cola. In this case, I think it would be #2 because it shows how many more people preferred it over Cola Nola, and that option makes Bolda Cola look a lot more popular than Cola Nola.

Stretching & Shrinking Problem 5.3

STretching & Shrinking Problem 5.3 Rr

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Using Triangles in real world measurments

5.1 & 5.2 Triangles

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Today in class we learned about how you can estimate heights and distances by using similar triangles. For instance, there is a telephone pole with a shadow of 5 ft. (length) There is a stick next to the telephone pole with a shadow of 1.25 ft. (length) The height of the stick is 2.5 ft. How tall is the telephone pole? the shadow next to the telephone pole makes a right triangle. The shadow next to the stick makes a right triangle. Because the sun is hitting the stick and the telephone pole at the same angle, the two triangles are similar. The telephone pole is 20 ft tall. I figured that out by finding the scale factor of the two triangles. Since I already have corresponding side measures and the height of the small triangle, I can figure it out. The corresponding side measures are 10 ft and 1.25 ft. To find the scale factor, I divided 10 by 1.25. That comes out to 8. Now I know that the scale factor from the smaller triangle to the larger
triangle is 8. To find the height of the telephone pole, I have to use the height of the smaller triangle. The height of the smaller triangle is 2.5 feet. I multiplied the height of the smaller triangle, (2.5 ft) by the scale factor (8). That equals 20 ft. That is the height of the telephone pole.

Ratios

Ratios

Today in class we learned about ratios. A ratio is a comparison between two quantities. You can compare numbers, side lengths, fruits to vegetables, you name it. Bottom line is that if it compares to quantities, its a ratio. An example of a ratio would be if you had five bananas and three apples, it would be a five to three ration or 5:3. You can also put ratios in fraction or decimal form. if you were comparing the numbers 7.3 and 9, you could write it as 7.3/9. Also, you can put that fraction into a decimal. 7.3/9 as a decimal is .81. sometimes you can't tell if a ratio is similar with another ratio unless you put it in decimal form. It's hard to tell if the ratios 11/13.5 and 18.3/22.5 are similar just by looking at them but if you put them into decimals they both equal .81.

by Quillen Bradlee

In class today we went over problem 4.1 and the homework. We learned that a parallelogram can not be similar if the corresponding angles are not the same, even if the ratios are equivalent. But for a rectangle the angles are always 90 degrees. That is what my class did today.

Similar polygons

Today we learned more about similar shapes. We reviewed the rules for telling weather two polygons are similar, which were equal angles, proportional sides, and the same basic shape. Finally, we learned how to find the angle measures and side lengths of one triangle, using it's similar shape. The picture to the left shows two similar triangles, UVY and XYZ. As you can see, all three of the corresponding angles are marked with the same number of arcs, which means that they are equal to eachother. The sides are also proplotinal to eachother. The scale factor of XYZ to UVW is two. This means that the are of XYZ is four times as large as the area of UVW. Finally, you can tell that they are similar because of their basic shape. This is one important rule used to find out if two shapes are similar.

Stretching & Shrinking Problem 3.3 wrap up

Stretching & Shrinking Wrap Up 3.3, Intro Mr Rr

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Stretching & Shrinking Problem 3.3

Stretching & Shrinking Problem 3.3 Rr

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Lesson 3.2

Today in class we learned about how to use rep-tile triangles to construct larger similar triangles. A rep-tile in math is any shape that, in a group with identical shapes can fit to gather to make a larger version of the shape. For example, a square is a rep-tile because if you fit four squares together it creates a larger square. An example for a non-rep-tile is a hexagon because no matter how many hexagons you fit together you can't create a larger hexagon. So today we split up into groups and each group recieved a bag of pattern-block triangles. Each group received a bag of either, isosceles, scalene, or right tringles. Then, each group would have to figure out how to use the given triangles to create a larger version of their triangles. We would use the information we found to answer questions in the "Stretching and Shrinking" book section 3.2 Afterwards, as a class we reviewed our answers and learned that all triangles are rep-tiles.

Stretching & Shrinking Reptile Triangles

Stretching & Shrinking 3.2 Wrap Up Rectangles

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Problem 3.1

In class today we learned about how larger shapes are similar to the original shape. For example If the original shape was a parallelogram the first lager similar shape would be 4 times larger than the original shape, 4 units would have been used and the scale factor would be 2. A good thing to remember is that in similar shapes the side lengths and perimeter change by the scale factor. Area of the original times the scale factor squared gives the area of the new shape. The definition of scale factor is the number used to multiply the lengths of a figure to stretch or shrink it to a similar image. For example if the scale factor was 3 all the lengths of the new image would be 3 times larger than the original image.

By Nicole Doherty

Stretching & Shrinking Problem 3.1 wrap up

Wrap Up 3.1 Intro 3.2 Rr

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