Question

A direct variation function contains the points (-8,-6) and (12, 9). Which equation represents the function?

Answer 1

Answer:

$y=\dfrac{3}{4}x$.

Step-by-step explanation:

The direct variation is defined as

$y\propto x$

$y=kx$

where, k is constant of proportionality.

It is given that a direct variation function contains the points (-8,-6) and (12, 9).

Substitute x=-8 and y=-6 in the above equation.

$-6=-8k$

Divide both sides by -8.

$\dfrac{-6}{-8}=k$

$\dfrac{3}{4}=k$

The value of constant of proportionality is $\dfrac{3}{4}$. So, the required equation is

$y=\dfrac{3}{4}x$

At x=12,

$y=\dfrac{3}{4}(12)=9$

It means, the line passing through (12,9). Hence, the equation is correct.

Therefore, the equation of the function is $y=\dfrac{3}{4}x$.