Question

Which lines are perpendicular to the line y – 1 = 1/3 (x+2)? Check all that apply.
y + 2 = –3(x – 4)
y − 5 = 3(x + 11)
y = -3x – 5/3
y = 1/3x – 2
3x + y = 7

Answer 1

The given line has slope (1/3).  Any new line perpendicular to the given line must therefore have slope -3, which is the negative reciprocal of (1/3).

Which of the given answer choices show slopes of -3?

Answer 2

Hey there! :) 

Which lines are perpendicular to y - 1 = 1/3(x + 2) ?

Well, we know that lines that are perpendicular to one another have slopes that are the negative reciprocal of one another, so we must find the negative reciprocal of our given slope.

1/3 → -3

So, let's look up at our answer choices - which lines have "-3" as the slope?

First, we must simplify all of answer choices.

y + 2 = -3(x - 4) → y + 2 = -3x + 12 → y = -3x + 10

y - 5 = 3(x + 11) → y - 5 = 3x + 33 → y = 3x + 28

y = -3x - 5/3 → already simplified.

3x + y = 7 → y = -3x + 7

Using these simplified equations, we now know which lines are perpendicular to our given line.

∵ y + 2 = -3(x - 4) 

∵ y = -3x - 5/3

∵ 3x + y = 7

Those bullet-ed equations are your answer! 

~Hope I helped!~