What is the average rate of change from x = −1 to x = 1?

when you write a linear equation as y = a*x, where you are relationing the numbers y to x, the rate of change from x to y is a.

then, the rate of change from -1 to 1 is the number that when multiplied by -1, turns into 1, so:

-1*a = 1

a = 1/-1 = -1

So the rate of change from x = -1 yo x = 1 is a = -1.

Your classmate incorrectly identified the sides that are proportional in the side-splitter theorem.

In this theorem, the segments formed on the traversal are proportional. However, in the diagram your friend is trying to prove that segments on the parallel lines are proportional. If he wanted to do that, he would need to have a different plan.