Question

for each equation, determine whether it shows a direct variation (that is, shows directly proportional variables).
if it does, find the constant of variation and write it in simplest form.

2y = -5x

○ direct variation
k =
○ not direct variation

4x + 5y = 0

○ direct variation
k =

Explanation:

Step1: Analyze \(2y = -5x\)

The form of direct variation is \(y = kx\) (where \(k\) is the constant of variation). For \(2y=-5x\), solve for \(y\) by dividing both sides by 2: \(y=\frac{-5}{2}x\). This is in the form \(y = kx\), so it is direct variation with \(k = -\frac{5}{2}\).

Step2: Analyze \(4x + 5y = 0\)

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

Answer:

For \(2y = -5x\):

• Direct variation
• \(k = -\frac{5}{2}\)

For \(4x + 5y = 0\):

• Direct variation
• \(k = -\frac{4}{5}\)