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?
OA. -3x+4y= 3
OB. 3x + 7y=63
OC. 2x+y=20
OD. 7x+3y= 70

Answer 1

B. 3x + 7y=63

Explanation:

You want the equation of the line through point (7, 6) that is perpendicular to the line -7x +3y = -21.5.

Perpendicular line

Perpendicular lines have slopes that are opposite reciprocals. When the equation of a line is given in the form ax +by = c, the perpendicular line can be written using the same coefficients as ...

bx -ay = c' . . . . . where c' is appropriate to the desired point

Here, that means the desired equation will have the form ...

3x +7y = c'

Only one answer choice has this form:

B. 3x +7y = 63

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Additional comment

We can verify the constant is correct using the point (x, y) = (7, 6).

3(7) +7(6) = 21 +42 = 63 . . . . matches the constant in the chosen equation

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