Answer:
y = (-3/2) - 4
Step-by-step explanation
2x - 3y = 13, when solved for -3y, results in -3y = -2x + 13. Then y = (2/3)x + C. Any line perpendicular to this y = (2/3)x + C has the slope which is the negative reciprocal of (2/3); that slope is -3/2.
Thus, the desired equation has the form y = (-3/2)x + b.
Subbing 5 for y and -6 for x, we get: 5 = (-3/2)(-6) + b, or 5 = 9 + b. Thus, b = -4, and so the equation of the line perpendicular to 2x - 3y = 13 is y = (-3/2) - 4.
