Question

Consider the line y=-5/9x+6

Find the equation of the line that is parallel to this line and passes through the point (9, -3).
Find the equation of the line that is perpendicular to this line and passes through the point (9, -3

Answer 1

See below in bold.

Explanation:

Use the point-slope form of a straight line

y - y1 = m(x - x1)

Here m = -5/9 , x1 = 9 and y1 = -3:, so

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

y + 3 = -5/9x + 5

y = -5/9x + 2 is the equation parallel to the given line.

The line perpendicular to the given line will have a slope of - 1 / -5/9

= 9/5 so its equation is

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

y = 9/5x - 81/5 - 3

y = 9/5x - 96/5 .