What is an equation of the line that passes through the point (4,2) (4,2) and is perpendicular to the line 4x+3y=21?

Answer 1

You can put 4x + 3y = 21 into Slope Intercept form as follows

3y = -4x + 21

y = (-4/3 )x + 7

The line above has a slope, m

m = (-4/3)

A line perpendicular to it would have a slope, m = (-1/m) where

(-1/m) = 3/4

In slope intercept form

y = (3/4)x + b

We can use the coordinates (4,2) to calculate b

2 = (3/4)(4) + b

2 = 3 + b

2 - 3 = b

-1 = b

The perpendicular line in Slope Intercept Form is

y = (3/4)x - 1

You can graph these lines a Desmos.com