# What is the equation of a line perpendicular to the line - 8x + y = - 56 and contains the point (8,7)?

Mar 2, 2018

solve for y
$y = 8 x - 56$

if a line is perpendicular, its slope is the negative reciprocal.
the slope of this equation is 8, so the slope of a line perpendicular to it is $- \frac{1}{8}$

plug this into the point-slope eqation
$y - 7 = - \frac{1}{8} \left(x - 8\right)$

this can be simplified to
$y = - \frac{1}{8} x + 8$