Answer:
[tex]y=-\frac{3}{2}x-5[/tex]
Step-by-step explanation:
First get the original equation to slope intercept form, [tex]y=\frac{2}{3}x[/tex]
Then, find the negative reciprocal of the slope. [tex]\frac{2}{3} -> \frac{-3}{2}[/tex]
Start building the new line in slope intercept form.
[tex]y-(-2) = (\frac{-3}{2} )(x-(-2))[/tex]
[tex]y+2=(\frac{-3}{2})(x+2)[/tex]
[tex]y+2-2=\frac{-3}{2}\left(x+2\right)-2[/tex]
[tex]y=-\frac{3}{2}x-5[/tex]
