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.