Question

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

Answer 1

we know that

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

With the point 1 or the point 2 find the value of the constant k

Point 1 (-8,-6)

x=-8

y=-6

substitute

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

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

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

therefore

the equation is

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

the answer is the option

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

Answer 2

Y=3/4x, as the sign of the function does not change, and the y value is less than the x value