The equation of the central street PQ is -1.5x - 3.5y = -31.5 option (b) is correct.
A straight line is a combination of endless points joined on both sides of the point.
We have a straight line:
[tex]-7x+3y=-21.5[/tex]
Convert it to the general form given below:
[tex]\rm y=mx+c[/tex]
[tex]\rm 3y=-21.5+7x\\\\ \rm y = \frac{-21.5}{3}+\frac{7}{3}x[/tex] or
[tex]\rm y = \frac{7}{3}x-\frac{21.5}{3}[/tex]
[tex]m = \frac{7}{3}[/tex] (Slope of AB line)
For the slope(m') of the PQ line:
[tex]\rm m'=-\frac{1}{m}[/tex] ( because AB and PQ are perpendicular to each other)
[tex]\rm m' = -\frac{3}{7}[/tex]
We know the:
[tex]\rm (y-y')=m'(x-x')[/tex]
Where (x', y') = (7, 6), we get:
[tex]\rm (y-6)=-\frac{3}{7} (x-7)[/tex]
[tex]\rm 7(y-6)=-3 (x-7)\\\\\rm 7y-42= -3x+21\\\\\rm 7y= -3x+21+42\\\\\rm 3x+7y=63[/tex]
[tex]\rm -1.5x-3.5y=-31.5[/tex] (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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