equation of perpendicular line

Question

write the equation for the line which is perpendicular to the line y=-3/2x+1 and which passes through the point (-6,-9)

Answer 1

The slope of the perpendicular line is the negative inverse of the given line or m=2/3 in this case.

Using the given point (-6,-9) in y-y₀= m(x-x₀).

y - (-9) = (2/3)(x- (-6)) = 2x/3 +4

y = 2x/3+4-9

y =2x/3-5

Answer 2

Hi Aliyah T

y = (2/3)x - 5

Perpendicular have inverse slopes of opposite signs, for your line which is already in slope intercept form

y = mx + b

y=-3/2x+1

The slope m = (-3/2)

A line perpendicular to it would have a slope of (2/3); notice it is the inverse and it is positive, and we can use it along with the coordinates given, (-6,-9) to solve for b and complete the line

y = (2/3)x + b

-9 = (2/3)(-6) + b

-9 = -4 + b

-9 + 4 = b

-5 = b

Your perpendicular line is

y = (2/3)x - 5

You can plot both lines at Desmos.com to confirm that they are perpendicular and your perpendicular line passes through the point (-6,-9) give it a try

Hope this helps you out.