Question

Find the slope of a line perpendicular to the line whose equation is 3x-2y=6 Fully simplify your answer.

Answer 1

Explanation:

First you need to convert this equation from standard form to slope-intercept form. To do that, subtract 3x from both sides so now you have 2y= -3x+6. Now, divide everything by 2 and you have your slope and y-intercept. Now to answer your question, all you need to do to find the perpendicular slope is change the negative/positive.

Slope of the Line: 3/2x

Final Equation: y = 3/2x + 3

Thank you!

Answer 2

Answer:
`- (2)/(3)`

Explanation:

So first, we re-arrange the equation of the line to make
`y\\` the subject:

`3x - 2y = 6\\-2y = -3x + 6\\2y = 3x - 6\\= > y = 1.5x - 3`

Now we have the line, we need to find the gradient of the line perpendicular to this line. To do this, we find the negative reciprocal of the gradient in
`y = 1.5x - 3` .

The negative reciprocal is basically when you multiply both gradients, you will have -1. So, for example,
`3/5` will become
`- 5/3` .

So in this question, the gradient is
`3/2`. The negative reciprocal of that will be
`- 2/3`.