Question

Tell whether the equation −2x + 4y = 5 represents a direct variation. If so, identify the constant of variation.

Answer 1

Direct variation is when y = mx + b ; b =0

-2x + 4y = 5

        4y = 2x + 5

         y = $\frac{2x}{4} + \frac{5}{4}$

It satisfies y = mx + b, where m = $\frac{2}{4} = \frac{1}{2}$  but doesn't satisy b = 0

Answer: NO

Answer 2

The equation of a direct variation is of the form
$y = mx$
But the given function can be rewritten as

$y = \frac{1}{2} x + \frac{5}{4}$
This is a partial variation,
$\frac{1}{2}$
is the constant of variation and

$\frac{5}{4}$
is the fixed constant.