Question

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

Answer 1

The equation of a direct variation is of the form

`y = mx`
But the given function can be rewritten as


`y = (1)/(2) x + (5)/(4)`
This is a partial variation,

`(1)/(2)`
is the constant of variation and


`(5)/(4)`
is the fixed constant.

Answer 2

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

-2x + 4y = 5

4y = 2x + 5

y =
`(2x)/(4) + (5)/(4)`

It satisfies y = mx + b, where m =
`(2)/(4) = (1)/(2)` but doesn't satisy b = 0

Answer: NO