Question

Mrs. Jackson gives the table below to her students.

X Y
4 26
5 23
6 M


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

For this case, the slope of the line is given by:

`a=(y2-y1)/(x2-x1)`

Substituting values, we have:

`a=(23-26)/(5-4)`

Rewriting:

`image`

Then, since the value of the slope is constant for a line then we can rewrite the slope equation to find the value of M.

We have then:

`-3 = (M-23)/(6-5)`

From here, we clear the value of M:

`image`

Answer:

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