Question

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

Answer 1

Answer:

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

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have the ordered pairs

(-9,-3) and (-12,-4)

Find the value of the constant of proportionality k

$k=\frac{y}{x}$

For x=-9, y=-3 ----> $k=\frac{-3}{-9}=\frac{1}{3}$

For x=-12, y=-4 ----> $k=\frac{-4}{-12}=\frac{1}{3}$

so

The value of k is equal to $\frac{1}{3}$

The linear equation is

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