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

The equation of the lane passing through A & B is $-7x+3y=-21.5$

This could be written as $\frac {7} {3}x -\frac {21.5} {3}$

Compare it with y=mx+c

$m=\frac {7} {3}$

$c=\frac {-21.5} {3}$

Central street PQ will be perpendicular to the lane passing through A & B. Product of slope of perpendicular lines will be$-1$

$m_1.m_2=-1$ so $m_2=\frac {-1} {m_1}$

$m_1=\frac {7} {3}$

Slope of perpendicular line $(m_2)=\frac {-1} {slope of parallel line (m_1)}$

$m_2=\frac {-1} {(\frac {7} {3} )}$

$m_2=\frac {-3} {7}$

Equation of line is $y=mx+c$

$y=\frac {-3} {7} x+c$

$7y+3x=7c$

PQ is passing through (7,6),so;

$7(6)+3(7)=7c$

$c=\frac {(41+21)} {7}$

$c=9$

So, Equation of Central street PQ is 

$3x+7y=7c$

$3x+7y=7(9)$

$3x+7y=63$