Exercise 25 Page 89

y = k x,

where

x

represents input values,

y

represents output values, and

k

represents the constant of variation. Let's consider the given function.

2 y = 3 x

Since the given function is not in the form of

y = k x,

let's try to rewrite it in this form by isolating

y .

2 y = 3 x

$LHS / 2 = RHS / 2$

y = \frac{3 x}{2}

$\frac{a \cdot b}{c} = \frac{a}{c} \cdot b$

y = \frac{2}{3} x

We were able to write the equation in the form

y = k x,

so we know that it is a direct variation. We can also identify the constant of variation.

y = \frac{2}{3} x

The constant of variation is

\frac{2}{3} .