Step by step
The question
Question: are y = 4x + 1 and y = 2x + 1 parallel, perpendicular or neither.
① y = 4x + 1 and ② y = 2x + 1
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 1.
m1 = 4
b = 1
2 Slope of ②
m is the number in front of x: 2.
It is the slope.
b is 1.
m2 = 2
b = 1
3 Compare the slopes
4 and 2 are not the same.
So the lines are not parallel.
4 ≠ 2
4 is 4/1.
Flip it: 1/4.
Then change the sign: −1/4.
4 = 41 → flip: 14
→ change the sign: −14
We get −1/4.
The second slope is 2.
Not the same.
−14 ≠ 2
So they are neither parallel nor perpendicular.
① and ② : neither
4 Check
Let's see it on the grid.
Draw both lines.
They meet, but not 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 : neither