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?\no $y = -\\frac{4}{3}x$\no $y = -\\frac{3}{4}x$\no $y = \\frac{3}{4}x$\no $y = \\frac{4}{3}x$

a direct variation function contains the points (-8, -6) and (12, 9). which equation represents the function?\no $y = -\\frac{4}{3}x$\no $y = -\\frac{3}{4}x$\no $y = \\frac{3}{4}x$\no $y = \\frac{4}{3}x$

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 a point

We can use either of the given points. Let's use the point $(12,9)$. Substitute $x = 12$ and $y = 9$ into $y=kx$. Then $9=k\times12$. Solving for $k$, we get $k=\frac{9}{12}=\frac{3}{4}$.

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