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?
a. -3x + 4y = 3
b.-1.5x − 3.5y = -31.5
c.2x + y = 20
d.-2.25x + y = -9.75

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,

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

Slope of line in Option A).

Slope =

So, this is not required equation.

Slope of line in Option B).

Slope =

So, this is required equation.

Therefore, Option B is correct .i.e., -1.5x - 3.5y = -31.5

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18