Question

A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?

Answer 1

Answer: third option.

Step-by-step explanation:

By definition, a direct variation function has the form shown below:

$y=kx$

Where k is a constant.

Then, knowing the given points, you can calculate k with the formula for calculate the slope of a line:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-(-3)}{-12-(-9)}=\frac{1}{3}$

Substituting k into  $y=kx$, you obtain:

$y=\frac{1}{3}x\\\\y=\frac{x}{3}$