# How do you determine whether the graph of absx=-3y is symmetric with respect to the x axis, y axis or neither?

Feb 13, 2017

Symmetric to y-axis;
Not symmetric to x-axis

#### Explanation:

If a relationship is symmetric to the y-axis then every point $\left(x , y\right)$ defined by that relationship is reflected through the y-axis as a point $\left(- x , y\right)$ which is also a member of that relationship.

That is if a relationship is symmetric to the y-axis, we can replace all occurrences of $x$ with $\left(- x\right)$ and the relationship will remain the same.

Given the relationship: $\left\mid x \right\mid = - 3 y$
since $\left\mid x \right\mid = \left\mid - x \right\mid$
$\left\mid x \right\mid = - 3 y \textcolor{w h i t e}{\text{XX}}$is identical to$\textcolor{w h i t e}{\text{XX}} \left\mid - x \right\mid = - 3 y$
and the relationship is symmetric to the y-axis

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Similarly, if a a relationship is symmetric to the x-axis, we can replace all occurrences of $y$ with $\left(- y\right)$ and the relationship will remain the same.

Given the relationship: $\left\mid x \right\mid = - 3 y$
we note that
$\left\mid x \right\mid = - 3 y \textcolor{w h i t e}{\text{XX}} i s \ast \neg \ast \equiv a \le n t \to$abs(x)=-3(-y)=+3y#
so the relationship is not symmetric to the x-axis.

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