Question

23.
Write an equation of the direct variation that includes the point (9, –12).

Answer 1

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:

\[
y = -\frac{4}{3}x
\]