Is $y = - x - 1$ $y = -x - 1$ a direct variation equation and if so what is the constant?

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Answer 1 · 2017-10-23T20:43:28

This is not a direct variation equation.

A direct variation requires that one variable varies at a constant rate with respect to another variable, i.e. they always have the same ratio:

$\frac{y}{x} = k$ $y/x =k$

Where $k$ $k$ is the constant of variation. This can be rearranged as:

$y = k x$ $y=kx$

This is similar to the equation for a line:

$y = m x + b$ $y=mx+b$

where $m = k$ $m=k$ and $b = 0$ $b=0$ . The question asks us if the following is a direct variation equation:

$y = - x - 1$ $y=-x-1$

which is a line with $m = - 1$ $m=-1$ and $b = - 1$ $b=-1$ . Since $b \neq 0$ $b!=0$ this is not a direct variation equation.

Please see the following link for more information and detail:
Direct Variation

Is y=−x−1y = -x - 1 a direct variation equation and if so what is the constant?