Question

write the equation of the line perpendicular to 2x-3y=6 through the point (-2,4)
please show work

Answer 1

Answer:

y = -3/2x + 1

Step-by-step 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:

$-3y = -2x+6\\y = \frac{2}{3}x - 2$

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)

$y = -\frac{3}{2} x - 3 + 4 \\y = -\frac{3}{2}x + 1$