What is equation represents a line which is perpendicular to the line 4x-3y=12

y = (-3/4)x + b

Step-by-step explanation:

If the slope of a given line is m, then the slope of any line perpendicular to the given line is the negative reciprocal of m:  -1/m.

First we need to calculate the slope of the given line, 4x - 3y = 12.  Dividing all three terms by -3, we get

y = (4/3)x - 4

and note that the slope of this line is 4/3.  Then the slope of any line perpendicular to this line is -3/4.

Then a general formula for a line perpendicular to 4x - 3y = 12 is

y = (-3/4)x + b, where the value of b depends upon the point on the given line through which the perpendicular ilne passes.