Does the equation represent a direct variation? If so, find the constant of variation: 5x = 3y.
Proportionality is an important concept which has many day-to-day uses. Various quantities can be compared using proportionality. For example, volume is inversely proportional to density.
Answer: The equation represents a direct variation, and the constant of variation for 5x = 3y is k = 5 / 3.
Let's understand the solution in detail.
Given: 5x = 3y
We can rearrange it as y = 5x / 3
Hence, we see that y ∝ x, and the equation is of the form y = kx, where k is the proportionality constant. This denotes that y varies directly with x.
Here k = 5 / 3.
Hence, the equation represents a direct variation, and the constant of variation is k = 5 / 3.