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

Answer:

$-1.5x-3.5y=-31.5$

Step-by-step 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

$-1.5x-3.5y=-31.5$