Question

Write the equation of the line perpendicular to 2x-3y=6 through the point (-2,4)

please show work

Answer 1

y = -3/2x + 1

Explanation:

Perpendicular lines' slope will have the negative reciprocal of the other one's slope.

First, put 2x-3y = 6 into slope - intercept form, so it would be:

`-3y = -2x+6\\y = (2)/(3)x - 2`

This means that the slope of that line is 2/3, so the slope of the perpendicular line would have to be -3/2.

Then, you can put this into point-slope form, so it would look like:

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

`y = -(3)/(2) x - 3 + 4 \\y = -(3)/(2)x + 1`