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?
A. -3x + 4y = 3
B.-1.5x − 3.5y = -31.5
C.2x + y = 20
D.-2.25x + y = -9.75

Answer 1

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,

$3y=7x+21.5$

$y=\frac{7}{3}+\frac{21.5}{3}$

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

$\frac{7}{3}\times m=-1$

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

Slope of line in Option A).

$4y=3x+3$

$y=\frac{3}{4}+\frac{3}{4}$

Slope = $\frac{3}{4}$

So, this is not required equation.

Slope of line in Option B).

$-3.5y=1.5x-31.5$

$y=\frac{1.5}{-3.5}+\frac{31.5}{3.5}$

Slope = $\frac{1.5}{-3.5}=\frac{3}{7}$

So, this is required equation.

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

Answer 2

-1.5x − 3.5y = -31.5