The graph of line $$m$$ is shown. ![](http://admin.getprephub.com/media/editor/gp15_20230225211109349466.png) What is the equation of the line that is perpendicular to line $$m$$ and passes through the point $$(-2,2)$$ ?

Answer The given line passes through $$(-2,2)$$ and $$(0,-3)$$ Slope of the line $$m=\frac{-3-2}{0-(-2)}=-\frac{5}{2}$$ Slope of the line perpendicular to the line $$m=-\frac{1}{(-\frac{5}{2})}=\frac{2}{5}$$ The equation of the required line is $$y-2=\frac{2}{5}(x+2)$$ or, $$5 y-10=2 x+4$$ or, $$2 x+10-4=5 y$$ or, $$y=\frac{1}{5}(2 x+6)$$ or, $$y=\frac{2}{5} x+\frac{6}{5}$$

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MCQ

The graph of line $m$ is shown.

What is the equation of the line that is perpendicular to line $m$ and passes through the point $(-2,2)$ ?

Select all that apply :

$y=\frac{2}{5} x+\frac{6}{5}$

$y=\frac{2}{5} x-\frac{4}{5}$

$y=\frac{1}{5} x+\frac{4}{5}$

$y=\frac{2}{5} x+\frac{2}{5}$

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