Is $y=2x+1$ a direct variation and if it is, how do you find the constant?

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Answer 1 · 2015-06-08T16:52:15

It is a direct variation and the constant of variation is the slope of the line, which is 2.

Answer 2 · 2015-06-08T17:00:16

Alternative view
$y= 2x +1$ is not a direct variation.

To be a direct variation multiplying one of $x$ or $y$ by some constant $k$ should cause the other to be multiplied by the same amount.

For example $(x,y) =(1, 3)$ is one solution pair for this equation.

If we let $k=5$
then
$color(white)("XXXX")$ $(5(1), 5(3)) = (5, 15)$ should also be a solution pair.

but $x=5$
$rArr y = 11$

So this is not a direct variation.

Note: $y=2x$ would be a direct variation.

Is y=2x+1y=2x+1 a direct variation and if it is, how do you find the constant?