Question

Mrs. Jackson gives the table below to her students.

Answer 1

M= 20 because the rate of change is -3.

Answer 2

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

$a=\frac{y2-y1}{x2-x1}$

Substituting values, we have:

$a=\frac{23-26}{5-4}$

Rewriting:

$a=\frac{-3}{1}\\a = -3$

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:

$-3 = \frac{M-23}{6-5}$

From here, we clear the value of M:

$-3 = \frac{M-23}{1}\\-3 = M - 23\\M = 23 - 3\\M = 20$

Answer:

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