Answer
Linear function.
Work Step by Step
The given equation is
$\Rightarrow y-x=2x-\frac{2}{3}y$
Multiply each side by $3$.
$\Rightarrow 3(y-x)=3(2x-\frac{2}{3}y)$
Use distributive property.
$\Rightarrow 3y-3x=6x-2y$
Add $2y+3x$ to each side.
$\Rightarrow 3y-3x+2y+3x=6x-2y+2y+3x$
Simplify.
$\Rightarrow 5y=9x$
Divide each side by $5$.
$\Rightarrow \frac{5y}{5}=\frac{9x}{5}$
Simplify.
$\Rightarrow y=\frac{9}{5}x$
$\Rightarrow y=\frac{9}{5}x+0$
The equation can be written as $y=mx+b$.
Hence, the given equation represent a linear function.
