Question

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

This is a PLATO math question, will give 15 pts to the best answer

Answer 1

Answer: B. -1.5x − 3.5y = -31.5

Explanation:

Answer 2

B. -1.5x − 3.5y = -31.5

Explanation:

You forgot to provide the reference image which is essential to answer the question, but I managed to find it... and attach it to my answer.

In the given equation for AB, if we place the y term on the left and x term on the right, we see the slope of that line is 7/3 (y = (7x - 21.5)/3 ==> 7/3x).

We see on the image that the line PQ is perpendicular to AB. That means that its slope is -3/7.

If we quickly check the slopes of each of the possible answers...

A. -3x + 4y = 3 ----> 4y = 3x - 3 ==> y = (3x-3)/4 => slope = 3/4

Not what we're looking for.

B. -1.5x - 3.5y = -31.5 ==> 3.5y = -1.5x + 31 ===> y = (-1.5x +31)/3.5

that gives us a slope of -1.5/3.5... We can simplify it... -3(0.5)/7(0.5) = -3/7

Exactly as predicted.

Since we have the point P (7,6), we can enter it in the equation to verify:

-1.5x - 3.5y = -31.5

-1.5 (7) - 3.5 (6) = -10.5 - 21 = -31.5 --- Verified

C. 2x + y = 20 ==> y = 20 - 2x ===> slope is -2, not what we want.

D. -2.25x + y = -9.75 ==> y = 2.25x - 9.75 ==> slop is 2.25 cannot be it.