Writing equations of lines parallel and perpendicular to a given line through a point

Question

Consider the line 

Find the equation of the line that is perpendicular to this line and passes through the point (−5,  2)

Find the equation of the line that is parallel to this line and passes through the point (−5,  2)

Answer 1

5x + 6y = -3

6y = -5x - 3

y = (-5/6)x - (1/2), the slope is -5/6

Parallel line has equal slope

Use point-slope form

(y + 3) = (-5/6)(x - 3)

Perpendicular line has slope of negative reciprocal

Use point-slope form

(y + 3) = (6/5)(x - 3)