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=-215. what is the equation of the central street pq? a. -3x + 4y = 3 b. 3x + 7y = 63 c. 2x + y = 20 d. 7x + 3y = 70

Explanation:

Step1: Find slope of line AB

Rewrite -7x + 3y=-21.5 in slope - intercept form y = mx + b. Add 7x to both sides: 3y=7x - 21.5. Then y=\frac{7}{3}x-\frac{21.5}{3}. The slope of line AB, m1=\frac{7}{3}.

Step2: Find slope of line PQ

Since line PQ is perpendicular to line AB, the product of their slopes is - 1. Let the slope of line PQ be m2. Then m1×m2=-1. So \frac{7}{3}×m2=-1, and m2 =-\frac{3}{7}.

Step3: Check slopes of options

For option A: -3x + 4y = 3, rewrite as y=\frac{3}{4}x+\frac{3}{4}, slope is \frac{3}{4}.
For option B: 3x + 7y = 63, rewrite as y=-\frac{3}{7}x + 9, slope is -\frac{3}{7}.
For option C: 2x + y = 20, rewrite as y=-2x + 20, slope is - 2.
For option D: 7x+3y = 70, rewrite as y=-\frac{7}{3}x+\frac{70}{3}, slope is -\frac{7}{3}.

Answer:

B. 3x + 7y = 63