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?

Question

anonymous · Answer

any help?

anonymous · Answer

-3x + 4y = 3

-1.5x − 3.5y = -31.5

2x + y = 20

-2.25x + y = -9.75

texaschic101 · Answer

is PQ parallel or perpendicular to AB

anonymous · Answer

perpindicular

texaschic101 · Answer

ok....perpendicular lines have negative reciprocal slopes.
So  first we find the slope of -7x + 3y = -21.5

3y = 7x - 21.5 -- divide by 3
y = 7/3x - 21.5/3

so the slope here is 7/3, but we need a negative reciprocal slope. To get that, we just flip the slope and change the sign.
So the slope for the perpendicular line is -3/7 (see how I flipped the slope and changed the sign).

-1.5x - 3.5y = -31.5 <--- this is your perpendicular equation
-3.5y = 1.5x - 31.5
y =  1.5/-3.5x - 31.5/-3.5
y = - 3/7x + 9 <--- it has a negative reciprocal slope