Step by step
The question
Question: are y = −4x + 2 and y = (1/4)x − 3 parallel, perpendicular or neither.
① y = −4x + 2 and ② y = 14x − 3
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: −4.
It is the slope.
b is 2.
m1 = −4
b = 2
2 Slope of ②
m is the number in front of x: 1/4.
It is the slope.
b is −3.
m2 = 14
b = −3
3 Compare the slopes
−4 and 1/4 are not the same.
So the lines are not parallel.
−4 ≠ 14
−4 is −4/1.
Flip it: −1/4.
Then change the sign: 1/4.
−4 = −41 → flip: −14
→ change the sign: 14
That is the second slope, 1/4!
14 = 14
Another way to check: multiply them.
−4 times 1/4 is −1.
Perpendicular slopes always multiply to −1.
−4 × 14 = −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