Asoftware 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?

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).