Answer:
[tex]y=-\frac{3}{2}x-12[/tex]
Step-by-step explanation:
Perpendicular lines have slopes which are negative reciprocals of each other. The slope of the line y=2/3x -3 is 2/3. The slope perpendicular to it is -3/2.
Using m=-3/2, substitute it and (-4,-6) into the point slope form and simplify to find the y-intercept.
[tex]y-y_1 = m(x-x_1)\\y--6=-\frac{3}{2}(x--4)\\y+6=-\frac{3}{2}(x+4)\\y+6=-\frac{3}{2}x-6\\y=-\frac{3}{2}x-12[/tex]
