Respuesta :
If we have an equation of the form
[tex]y=mx+b[/tex]then the equation of the perpendicular line is given by
[tex]y=-\frac{1}{m}x+c[/tex]Now, keeping that in mind, the equation of the perpendicular line to y =-8x+7 is
[tex]y=\frac{1}{8}x+c[/tex]We find c by using the fact that this perpendicular line passes through (-6, -5)
Putting in x = -6 and y = -5 gives
[tex]-5=\frac{1}{8}(-6)+c[/tex][tex]-5-\frac{3}{4}=c[/tex][tex]c=-\frac{23}{4}[/tex]Hence, the equation of the perpendicular line is
[tex]y=-\frac{1}{8}x-\frac{23}{4}[/tex]The equation of the parallel line is
[tex]y=-8x+b[/tex]We find b using the point (-6, -5). Putting tn x = -6 and y = -5 gives
[tex]-5=-8(-6)+b[/tex][tex]b=43[/tex]Hence, the equation of the parallel line is
[tex]y=-8x+43[/tex]
