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

Answer 1

The equation of the central street PQ is  -1.5x - 3.5y = -31.5 option (b) is correct.

What is a straight line?

A straight line is a combination of endless points joined on both sides of the point.

We have a straight line:

$-7x+3y=-21.5$  

Convert it to the general form given below:

$\rm y=mx+c$

$\rm 3y=-21.5+7x\\\\ \rm y = \frac{-21.5}{3}+\frac{7}{3}x$ or

$\rm y = \frac{7}{3}x-\frac{21.5}{3}$

$m = \frac{7}{3}$   (Slope of AB line)

For the slope(m') of the PQ line:

$\rm m'=-\frac{1}{m}$    ( because AB and PQ are perpendicular to each other)

$\rm m' = -\frac{3}{7}$

We know the:

$\rm (y-y')=m'(x-x')$

Where (x', y') = (7, 6), we get:

$\rm (y-6)=-\frac{3}{7} (x-7)$

$\rm 7(y-6)=-3 (x-7)\\\\\rm 7y-42= -3x+21\\\\\rm 7y= -3x+21+42\\\\\rm 3x+7y=63$

$\rm -1.5x-3.5y=-31.5$   (multiply by -1/2 on both sides)

Thus, the equation of the central street PQ is  -1.5x - 3.5y = -31.5

Learn more about the straight line.

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