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.

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

Substituting values, we have:

Rewriting:

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:

From here, we clear the value of M:

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

question:

could we have options?

is only a line? i think so