Write the equation of a line perpendicular to 4x + 3y =-8. with an x intercept of (12,-15)?

You would have to find the slope of the equation first.
4x+3y=-8
-4x       -4x
3y=-4x-8
_   
3       3
y=-4/3x-8

For a line to be perpendicular to another line, the slope,m, of the new equation would need to be the negative reciprocal of the original. To put it short, take the fraction, flip it, and multiply it by -1.

original m=-4/3
perpendicular m= 3/4

You would use the slope-intercept form to solve for the new equation.

y1=y value
x1= x value

y-y1=m(x-x1)
y-(-15)=3/4(x-12)

distribute:
y+15=3/4x-9

then solve for y:
y+15=3/4x-9
  -15        -15
y=3/4x-24