a direct variation function contains the points (-8, -6) and (12, 9). which equation represents the…

a direct variation function contains the points (-8, -6) and (12, 9). which equation represents the function?\n$y = -\\frac{4}{3}x$\n$y = -\\frac{3}{4}x$\n$y = \\frac{3}{4}x$\n$y = \\frac{4}{3}x$

a direct variation function contains the points (-8, -6) and (12, 9). which equation represents the function?\n$y = -\\frac{4}{3}x$\n$y = -\\frac{3}{4}x$\n$y = \\frac{3}{4}x$\n$y = \\frac{4}{3}x$

Answer

Explanation:

Step1: Recall direct - variation formula

The formula for a direct - variation function is $y = kx$, where $k$ is the constant of variation.

Step2: Find the value of $k$ using one of the points

We can use the point $(x,y)=( - 8,-6)$. Substitute into $y = kx$: $-6=k\times(-8)$ $k=\frac{-6}{-8}=\frac{3}{4}$ We can also use the point $(12,9)$. Substitute into $y = kx$: $9 = k\times12$ $k=\frac{9}{12}=\frac{3}{4}$

Step3: Write the equation of the function

Since $k = \frac{3}{4}$, the equation of the direct - variation function is $y=\frac{3}{4}x$.

Answer:

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