Question

Mrs. Jackson gives the table below to her students.

In order for the function to be linear, what must m be and why?
m = 22 because the rate of change is 1.
m = 20 because the rate of change is 3.
m = 22 because the rate of change is –1.
m = 20 because the rate of change is –3.

Answer 1

According to the table, if x increases by 1 from 4 to 5, y decreases by 3.

Also, if x increases by 1 from 5 to 6, y must be 3 less than 23, or 20, for all 3 points to be collinear.

m = 20 because the rate of change is –3.

Answer 2

The answer is m = 20 because the rate of change is –3.

We can see that the difference between 26 and 23 is 3. Because the values are going down as x goes up, that means the change is negative. Therefore, the rate of change is -3.