Answer:
[tex]y=\frac{5}{2}x-13[/tex]
Step-by-step explanation:
Given the equation
[tex]y=-\frac{2}{5}x-1[/tex]
comparing the equation with the slope-intercept form[tex]y=mx+b[/tex]
Here,
so the slope of the line is m = -2/5
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line,
so the slope of the perpendicular line will be: 5/2
Therefore, the point-slope form of the equation of the perpendicular line that goes through (2,-8) is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-8\right)=\frac{5}{2}\left(x-2\right)[/tex]
[tex]y+8=\frac{5}{2}\left(x-2\right)[/tex]
subtract 8 from both sides
[tex]y+8-8=\frac{5}{2}\left(x-2\right)-8[/tex]
[tex]y=\frac{5}{2}x-13[/tex]
