Question

Identify an equation in point-slope form for the line perpendicular to y = –2x + 8 that passes through (–3, 9).

Answer 1

For this case we have the following linear equation:
 $y = -2x + 8$
 As the lines are perpendicular, then the slope of the line is:
 $m' = \frac{-1}{m}$
 Where,
 m: is the slope of the original line
 Substituting values we have:
 $m' = \frac{-1}{-2}$
 Rewriting:
 $m' = \frac{1}{2}$
 Then, the equation in point-slope form is given by:
 $y-yo = m '(x-xo)$
 Where,
 (xo, yo): ordered pair that goes through the line.
 Substituting values we have:
 $y-9 = \frac{1}{2}(x+3)$
 Answer:
 an equation in point-slope form for the line perpendicular to y = –2x + 8 that passes through (–3, 9) is:
 $y-9 = \frac{1}{2}(x+3)$