Question

A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?
y = –4/3x
y = –3/4x
y = 3/4x
y =4/3 x

Answer 1

Answer:

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

Step-by-step explanation:

If it is a direct variation function, then $\frac{y}{x}=k$.

$k$ can be found by choosing a point and doing $y$ divided by $x$.

So we can find $k$ by doing -6 divided by -8 or 9 divided by 12.

Both of these values are equal to 0.75 or 3/4 as a fraction.

So you can say any point in this relation will follow the equation:

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

Multiply both sides by $x$:

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