14.

Write an equation of the direct variation that includes the point (6, –2).

1 answer

In a direct variation, the relationship between two variables \( y \) and \( x \) can be expressed with the equation:

\[ y = kx \]

where \( k \) is the constant of variation. To find \( k \), we can use the point (6, –2).

Substituting \( x = 6 \) and \( y = -2 \) into the equation:

\[ -2 = k(6) \]

Now, solve for \( k \):

\[ k = \frac{-2}{6} = -\frac{1}{3} \]

Now that we have found \( k \), we can write the equation of the direct variation:

\[ y = -\frac{1}{3}x \]

So, the equation of the direct variation that includes the point (6, –2) is:

\[ y = -\frac{1}{3}x \]