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?

See attachment below for picture/answer choices

Answer 1

its B -1.5x − 3.5y = -31.5

Answer 2

`-1.5x-3.5y=-31.5`

Explanation:

we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

so

`m1*m2=-1`

In this problem line AB and line PQ are perpendicular

Step 1

Find the slope of the line AB

The equation of the line AB is

`-7x+3y=-21.5`

isolate the variable y

`3y=7x-21.5` ------>
`y=(7/3)x-21.5/3`

The slope of the line AB is equal to

`m1=7/3`

Step 2

Find the slope of the line PQ

remember that

`m1*m2=-1`

we have

`m1=7/3` ----> slope line AB

so

substitute and solve for m2

`(7/3)*m2=-1`

`m2=-3/7`

Step 3

Find the equation of the line PQ

The equation of the line into point-slope form is equal to

`y-y1=m(x-x1)`

we have

`m=-3/7`

`P(7,6)`

substitute

`y-6=(-3/7)(x-7)`

`y=(-3/7)x+3+6`

`y=(-3/7)x+9` -----> multiply by
`7` both sides

`7y=-3x+63`

`7y+3x=63` -----> divide by
`2` both sides

`1.5x+3.5y=31.5` -----> multiply by
`-1` both sides

`-1.5x-3.5y=-31.5`