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?

Answer 1

Interesting Question
What you are being asked is What is the line Perpendicular to AB going through point (7,6)

Step One
What is the slope of the given line
-7x + 3y = -21.5     Add 7x to both sides.
3y = 7x - 21.5        Divide by 3
y = 7x/3 - 21.5/3

The slope of the given line is 7/3 (just read it)

Step Two
What is the slope of the line perpendicular to it.

The slopes are connect by the formula
m1 * m2 = - 1
m1 = 7/3
7/3 * m2 = - 1 Multiply by 3/7
m2 = - 1 * 3/7
m2 = - 3/7

Step three
Find the y intercept, where b in the equation below is the y intercept..
y = -3/7 x + b
y = 6
x = 7
6 = -3/7 * 7 + b
6 = -3 + b    Add 3 to both sides.
6 + 3 = b 
b = 9

Step Three
State the equation
y = - 3/7 x + 9

Now you have to juggle the numbers to get the answer. 

Step 4
put the -3/7 x on the left side.
y + 3/7 x = 9     Multiply both sides by 7
7y + 3x = 63     Now for some strange reason, you divide by 2
3.5y + 1.5x = 31.5  The answer is the second one down (middle one).