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