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
[tex]m=\frac{2}{5}[/tex]So, the slope of a line perpendicular to the line y= 2/5 x+2 is
[tex]m_1=\frac{1}{m}=\frac{-1}{\frac{2}{5}}=\frac{-5}{2}[/tex]The slope intercept form for a line passing through the point (x1,y1) and having slope m1 is
[tex]\frac{y_1-y}{x_1-x}=m_1[/tex]The point given is
[tex](x_1,y_1)=(2,-2)[/tex]Also the slope for the line is -5/2 as obtained above. So
[tex]\begin{gathered} \frac{-2-y}{2-x}=\frac{-5}{2} \\ (-2-y)2=-5(2-x) \\ -4-2y=-10+5x \\ -4+10=5x+2y \\ 5x+2y=6 \end{gathered}[/tex]The equation is 5x+2y=6.
