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

easiest way:

since the 2 lines must be perpendicular, the new equation must look like

9x + 2y = c
Plug in (-2,3)
-18 + 6 = c
c = -12

equation is : 9x + 2y = -12
in slope-intercept form:
2y = -9x - 12
y = (-9/2)x - 6