Find the equation of a line that is perpendicular

Question

Find the equation of the line that is perpendicular to the line "-3x+2y=10" and goes through the point (0,8)

Answer 1

First write in slope intercept form:

-3x+2y=10

+3x +3x

2y/2=(3x+10)/2

y=3/2x+10/2

y=3/2x+5

original slope is 3/2, perpendicular slope is negative reciprocal : -2/3

Use the point to find the equation of the line, this one is easy because the point given is the y-intercept.

y=mx+b

m=-2/3

b=8

y=-2/3x+8 => this is the line perpendicular to the original that goes through the given point.

Answer 2

First, we need to find the slope of the perpendicular line, which is the negative reciprocal of the slope of this line. If we convert this line to slope-intercept form, we get:

y = (3/2)x + 5

Therefore, the slope of this line is 3/2, and the slope of the perpendicular line must be -2/3. We were given the y-intercept (0,8), therefore the equation of the line is:

y = (-2/3)x + 8