Question

for the direct variation. then find each value. 8. if $y = -12$ when $x = 9$, find $y$ when $x = -4$.

Explanation:

Step1: Recall direct variation formula

For direct variation, the formula is \( y = kx \), where \( k \) is the constant of variation. We first need to find \( k \) using the given values \( y = -12 \) and \( x = 9 \).

Substitute \( y = -12 \) and \( x = 9 \) into \( y = kx \):
\( -12 = k \times 9 \)

Step2: Solve for \( k \)

To find \( k \), divide both sides of the equation by 9:
\( k=\frac{-12}{9}=-\frac{4}{3} \)

Step3: Find \( y \) when \( x = -4 \)

Now that we have \( k = -\frac{4}{3} \), we use the direct variation formula \( y = kx \) again. Substitute \( k = -\frac{4}{3} \) and \( x = -4 \) into the formula:
\( y=-\frac{4}{3}\times(-4) \)
\( y = \frac{16}{3} \)

Answer:

\( \frac{16}{3} \)