Answer:
Option B is correct .i.e., -1.5x - 3.5y = -31.5
Step-by-step explanation:
Given: All streets are either parallel or perpendicular.
Equation of Street AB , -7x + 3y = 21.5
To find Equation of Street PQ
Re write the given equation in form of slope and intercept form
we get,
[tex]3y=7x+21.5[/tex]
[tex]y=\frac{7}{3}+\frac{21.5}{3}[/tex]
From this slope of street AB is [tex\frac{7}{3}[/tex].
From given pic Street PQ is perpendicular to street AB.
we know that product of slope of perpendicular lines should be equal to -1
let slope of PQ = m
[tex]\frac{7}{3}\times m=-1[/tex]
[tex]m=\frac{-3}{7}[/tex]
Slope of line in Option A).
[tex]4y=3x+3[/tex]
[tex]y=\frac{3}{4}+\frac{3}{4}[/tex]
Slope = [tex]\frac{3}{4}[/tex]
So, this is not required equation.
Slope of line in Option B).
[tex]-3.5y=1.5x-31.5[/tex]
[tex]y=\frac{1.5}{-3.5}+\frac{31.5}{3.5}[/tex]
Slope = [tex]\frac{1.5}{-3.5}=\frac{3}{7}[/tex]
So, this is required equation.
Therefore, Option B is correct .i.e., -1.5x - 3.5y = -31.5
