Question

What is the equation of the line perpendicular to y=2/3x+1 that passes through the point (12, –6)?

A. 3x + 2y = 24
B. 3x + 2y = 6
C. 2x – 3y = 42
D. 2x – 3y = –48

Answer 1

The answer is A. Get y by itself. Y=-3/2x+ 12
Then place 12 in for x and -6 for y

Answer 2

Explanation:

Start with y=(2/3)x+1 . The slope of any line perpendicular to this is the negative reciprocal of 2/3: -3/2.

Then we have y = mx + b, which, using the given data (12, -6), becomes

-6 = (-3/2)(12) + b, or

-6 = -18 + b, so b = 12 and y = (3/2)x + 12.

We must put this into standard form. Mult. all three terms by 2:

2y = 3x + 24