Write the equation of the line with the given properties: passing thru (4,-2) and perpendicular to the line 3x-2y=-1. write the equation in slop intercept form

To be perpendicular to the given line, the slope has to be 3/2, which you can find by rewriting the equation in y=... form. Now all we have to find is a constant b to make y=3/2x + b pass through (4,-2).

Fill in this point:

-2 = 3/2*4 + b => b = -6-2 = -8.

So the equation is y=3/2x - 8