Question

got it? does $4x + 5y = 0$ represent a direct variation? if so, find the constant of variation.

Explanation:

Step1: Recall direct variation form

The form of direct variation is \( y = kx \), where \( k \) is the constant of variation. We need to rewrite \( 4x + 5y = 0 \) in this form.

Step2: Solve for \( y \)

Subtract \( 4x \) from both sides: \( 5y=-4x \)
Divide both sides by 5: \( y = -\frac{4}{5}x \)
This is in the form \( y = kx \) with \( k = -\frac{4}{5} \), so it is a direct variation.

Answer:

Yes, the constant of variation is \(-\frac{4}{5}\)