Question

what is the equation, in slope intercept form, of the line that is perpendicular to the line y - 4 = 2/3 (x -6) and passes through the point -2/-2

Answer 1

Answer:

$y=-\frac{3}{2}x-5$

Step-by-step explanation:

First get the original equation to slope intercept form, $y=\frac{2}{3}x$

Then, find the negative reciprocal of the slope. $\frac{2}{3} -> \frac{-3}{2}$

Start building the new line in slope intercept form.

$y-(-2) = (\frac{-3}{2} )(x-(-2))$

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

$y+2-2=\frac{-3}{2}\left(x+2\right)-2$

$y=-\frac{3}{2}x-5$