What is the equation of the central street PQ?

Question

Select the correct answer.

A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?

A. 

-3x + 4y = 3

B. 

-1.5x − 3.5y = -31.5

C. 

2x + y = 20

D. 

-2.25x + y = -9.75

Answer 1

Equation for AB line:

-7x + 3y = -21.5

Solve for "y":

y = (7/3)x - (21.5)/3 → Slope-Intercept form

m = 7/3 → slope of line AB

Line PQ is perpendicular to line AB. It has point P: (7, 6)

m_PQ = -1/m = -3/7 → slope of a line perpendicular to another line with a known slope

Write equation for PQ:

(y - 6) = (-3/7)(x - 7) → multiply by "-7"

-3x -7y = -63

Divided by "2":

-1.5x -3.5y = -31.5

Answer: B

Answer 2

m AB = 7 / 3

m PQ = -3 / 7

Which choice has the slope of -3 / 7?