Question

Line j goes through the point (-7, 5) and is perpendicular to 2x – 3y = -18. Find the equation of line j.

Answer 1

Answer:

3x + 2y = 31  

Step-by-step 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.