Question

Does the equation represent a direct variation? If so, find the constant of variation.

5x = -3y

A. yes; k = 3/5
B. no
C. yes; k = 5/3
D. yes; k = -5/3

Answer 1

if there is a direct variation for y and x, you can say y is proportional to x.

Answer 2

y is proportional and varies directly with x
\[\large y~~\alpha~~x\]
put in a proportionality constant k to make an equation.
\[\large y=k*x\]

Answer 3

Solving this given equation for y
5x = -3y

\[y=-\frac{ 5 }{ 3 }*x\]

You see it is a direct variation y=k*x, with k being -5/3

Answer 4

as opposed to an inverse variation, if y varies inversely with x, then you have
\[\large y~~\alpha~~\frac{ 1 }{ x }\]
\[\large y=\frac{ k }{ x }\]