Step by step
The question
Question: are y = −x + 5 and y = x − 2 parallel, perpendicular or neither.
① y = −x + 5 and ② y = x − 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
1 Slope of ①
m is the number in front of x: −1.
It is the slope.
b is 5.
m1 = −1
b = 5
2 Slope of ②
m is the number in front of x: 1.
It is the slope.
b is −2.
m2 = 1
b = −2
3 Compare the slopes
−1 and 1 are not the same.
So the lines are not parallel.
−1 ≠ 1
−1 is −1/1.
Flip it: −1/1.
Then change the sign: 1.
−1 = −11 → flip: −11
→ change the sign: 1
That is the second slope, 1!
1 = 1
Another way to check: multiply them.
−1 times 1 is −1.
Perpendicular slopes always multiply to −1.
−1 × 1 = −1
perpendicular slopes multiply to −1
So the lines are perpendicular: they meet at a square corner.
① and ② are perpendicular
4 Check
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