Is the rate of change of the function 5?

"No, because y does not change by 5 every time x changes by 1"

Step-by-step explanation:

It is easy to calculate the rate of change of a function when they give you a graph. Just locate yourself on one point on the line whose coordinates are easy to read (for example the point (0, -2) in this graph that is located on the y axis 2 units below the origin of coordinates)

Recall that the rate of change tells you the "rise over the run". That is how many units (up or down) the function changes as you move to the right  certain number of units.

It is very simple to find that rate of change when we move one unit to the right. Notice that as you move from (0, -2) one unit to the right (to x=1), in order to find the y-value associated with it on the line, you need to go to the point (1, 2) which forces you to move as well 4 units up (from -2 to 2).

Therefore the rate of change here is 4/1 = 4, and not 5.

So the correct answer is the third option given in the list:

"No, because y does not change by 5 every time x changes by 1"