Question

help please! find the equation of the line perpendicular to 2x+3y-9=0 that passes thru the origin. thanks :)

Answer 1

slope is opposite reciprocal of -2/3 --> 3/2
passes through origin implies y-intercept of 0
y = 3/2x

Answer 2

slope is opposite reciprocal of -2/3 --> 3/2 passes through origin implies y-intercept of 0 y = 3/2x

Answer 3

Perpendicular line will have a slopes which are negative reciprocals of eachother. And to go through the origin, y has to equal 0 when x is 0.

Answer 4

thanks everyone! :D

Answer 5

The slope of the perpendicular line will be the negative reciprocal of the slope of the original line (2x+3y-9=0). First, you need to rewrite the equation from standard form ax+by-c=0 to slope-intercept form y=mx+b.

2x+3y-9=0 <---- ax+by+c=0
2x+3y-9+9=0+9
2x+3y=9
2x-2x+3y=9-2x
3y=9-2x
3y=9-2x
--- -----
3 3
y=3-2/3x OR y=-2/3x+3 <---- the same equation but in y=mx+b

So your slope is -2/3. The perpendicular line will have a slope that is the negative reciprocal of -2/3, which is 1.5. (You just find the reciprocal of -2/3, which is -3/2 or -1.5, and turn it negative, but because -1.5 is already negative, it turns positive.)
The slope of the perpendicular line is 1.5, so your equation right now looks like this:
y=1.5x+b
Because the line passes through the origin, the y-intercept will be (0,0). This means that b=0. So your equation is y=1.5x.
Hope that cleared it up and can help with this kind of problem in the future!

Answer 6

hi kate