Answer
$y=\frac{2}{3}x+\frac{4}{3}$
Work Step by Step
The given point is $(-5,-2)$.
The given equation of the line is
$\Rightarrow y=\frac{2}{3}x+1$
Slope of the line is $m=\frac{2}{3}$.
Slope of the parallel line is $m=\frac{2}{3}$.
The slope-intercept form is
$\Rightarrow y=mx+b$
Substitute $\frac{2}{3}$ for $m,-5$ for $x,$ and $-2$ for $y$.
$\Rightarrow -2=\frac{2}{3}(-5)+b$
Simplify.
$\Rightarrow -2=-\frac{10}{3}+b$
Add $\frac{10}{3}$ to each side.
$\Rightarrow -2+\frac{10}{3}=-\frac{10}{3}+b+\frac{10}{3}$
Simplify.
$\Rightarrow \frac{-6+10}{3}=b$
$\Rightarrow \frac{4}{3}=b$
The equation of the parallel line is
$\Rightarrow y=\frac{2}{3}x+\frac{4}{3}$.
