To find a perpendicular line, find the opposite reciprocal of the slope of the line. The opposite reciprocal of 3/4 is -4/3. The slope of the new line will thus be -4/3.
We can determine from a line with this slope that it will pass through (12, 7) with a y-intercept of 23, so:
The equation of the line is -4/3x + 23.