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What Is the equation in the slope- intercept form of the line that passes through (2,-2) and is perpendicular to the line resprsented by y= 2/5 x+2

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The slope of line perpendicular to the line with slope m is -1/m.

The line y=2/5 x+2 is in the form of the equation y=mx+c.

So, comparing equations, we get


m=(2)/(5)

So, the slope of a line perpendicular to the line y= 2/5 x+2​ is


m_1=(1)/(m)=(-1)/((2)/(5))=(-5)/(2)

The slope intercept form for a line passing through the point (x1,y1) and having slope m1 is


(y_1-y)/(x_1-x)=m_1

The point given is


(x_1,y_1)=(2,-2)

Also the slope for the line is -5/2 as obtained above. So


\begin{gathered} (-2-y)/(2-x)=(-5)/(2) \\ (-2-y)2=-5(2-x) \\ -4-2y=-10+5x \\ -4+10=5x+2y \\ 5x+2y=6 \end{gathered}

The equation is 5x+2y=6.

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