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