Question

1. if y = -6 when x = -14, find x when y = -4.

Explanation:

Step1: Assume direct variation (y = kx)

First, we find the constant of variation \( k \) using the given values \( y = -6 \) and \( x = -14 \). Substitute into \( y = kx \):
\( -6 = k(-14) \)

Step2: Solve for k

To find \( k \), divide both sides by \( -14 \):
\( k=\frac{-6}{-14}=\frac{3}{7} \)

Step3: Find x when y = -4

Now that we know \( k = \frac{3}{7} \), use the equation \( y = kx \) with \( y = -4 \) to find \( x \). Substitute \( y = -4 \) and \( k=\frac{3}{7} \) into \( y = kx \):
\( -4=\frac{3}{7}x \)
Multiply both sides by \( \frac{7}{3} \) to solve for \( x \):
\( x=-4\times\frac{7}{3}=-\frac{28}{3} \)

Answer:

\( x = -\frac{28}{3} \)