In direct variation, the relationship between two variables \( x \) and \( y \) can be expressed as:
\[ y = kx \]
where \( k \) is the constant of variation. To find the value of \( k \), we can use the point \((9, -12)\).
Substituting \( x = 9 \) and \( y = -12 \) into the equation gives:
\[ -12 = k \cdot 9 \]
Now, solve for \( k \):
\[ k = \frac{-12}{9} = -\frac{4}{3} \]
Now that we have the value for \( k \), we can write the equation of the direct variation:
\[ y = -\frac{4}{3}x \]
Therefore, the equation of the direct variation that includes the point (9, –12) is:
\[ y = -\frac{4}{3}x \]