Write the slope-intercept equation for the line that passes through (-2,3) and is perpendicular to 2x-9y=-12

-9y = -2x - 12 we need to put this in y = mx + b form so by moving our variables around and solving for y we get:

y = 2/9x + 4/3   2/9 is our slope. A perpendicular line will have a neg. reciprocal slope so the slope we need is -9/2.

We take that slope and our point and plug in to point-slope form to find new equation

y - 3 = -9/2(x - -2)

y - 3 = -9/2 (x + 2)

y - 3 = -9/2x + -9

y - 3 = -9/2x - 9

y = -9/2x - 6