Are x = 3 and y = -2 parallel, perpendicular or neither

Step by step, with the reason for every step · Parallel and perpendicular lines · Algebra 1

Step by step

Question: are x = 3 and y = −2 parallel, perpendicular or neither.

① x = 3 and ② y = −2

The slopes tell us which.

Same slope: parallel.

Flip the slope and change its sign: perpendicular.

parallel: same slope

perpendicular: flip and change the sign

x = 3 is a vertical line: straight up and down.

We call its slope undefined.

m₁ = undefined

There is no x term.

So m = 0: a flat line.

b is −2.

m₂ = 0

b = −2

One line is vertical, the other is flat.

A vertical line and a flat line always meet at a square corner.

undefined and 0

So the lines are perpendicular: they meet at a square corner.

① and ② are perpendicular

Let's see it on the grid.

Draw both lines.

They meet at a square corner.

Let's look back.

First: slope of ①.

Then: slope of ②.

Then: compare the slopes.

Last: check.

Answer

① and ② are perpendicular

Try this one yourself, then check:

Are ① x = −1 and ② y = 4

Show the answer

perpendicular