Find the equation of the line in slope intercept form that is perpendicular to 2x-3y-12=0 and passes through the point (-3, 5). show your work
+238 Rearrange the equation into slope-intercept form,
\(-3y = -2x+12 \\ y = \frac{2}{3}x -4\)
The line we are looking for is perpendicular meaning that it's slope is the negative and reciprocal of $\frac{2}{3}$,
\(y = -\frac{3}{2}x + b\)
We know it passes through (-3, 5) so we can plug that in,
\(5 = \frac{9}{2} + b \\ b = \frac{1}{2}\)
So our final equation for the line we are looking for is \(y = -\frac{3}{2}x + \frac{1}{2}\)
