Answer:
3x + 2y = 31
Explanation:
Solve the given equation for y to determine the slope of this line:
-3y = -2x = -18, so that y = (2/3)x + 6.
Therefore, a line perpendicular to the given line has the slope -3/2, which is the negative reciprocal of this 2/3.
Using the slope-intercept formula y = mx + b and inserting the knowns (slope = m = -3/2, y = 5 and x = -7), we obtain:
5 = (3/2)(-7) + b, or (after multiplying all terms by 2):
10 = -21 + 2b, or 2b = 31, or b = 31/2.
Then the equation is y = (-3/2)x + 31/2.
Let's put this into standard form. Multiply all terms by 2, obtaining:
2y = -3x + 31, or
3x + 2y = 31 This is the equation of the perpendicular line in question.