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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 software designer is mapping the streets for a new racing game. All of the streets-example-1

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Answer:

y = (-3/7)x + 9 ( -1.5x − 3.5y = -31.5)

Explanation:

Normally, there's a list of possible answers associated to this question, and the answer is usually in the form of -1.5x − 3.5y = -31.5 (equivalent to y = (-3/7)x + 9)

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.

So, we have a slope of -3/7 and we know it passes through point P (7,6), let's see if we can find the missing term.

y = (-3/7) x + b

6 = (-3/7) 7 + b

6 = -3 + b

b = 9

So the equation of the line forming the street PQ is y = (-3/7)x + 9

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