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 parallel to this line and passes through the point 

(5,  3)

Find the equation of the line that is perpendicular to this line and passes through the point 

(5,  3)

Answer 1

Parallel lines have the same slope:

Use point-slope form

y - 3 = (9/5)(x - 5)

Perpendicula lines have slopes that are negative reciprocals

Use point-slope form

y - 3 = (-5/9)(x - 5)