Question

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

Answer 1

The direct variation equation has the form y=kx, where k is the constant of variation. We can find the value of k by substituting the values for x and y using any given point such as (9, -12) and solving for k.\[-12=k*9\]or\[k=\frac{-12}{9}=\frac{-4*\cancel3}{3*\cancel3}=\frac{-4}{3}\]Now we can write y=kx with the found constant of variation:\[y=-\frac{4}{3}x\]
This is an equation of the direct variation that includes the point (9, –12).