Step by step
The question
Question: are y = 2x + 1 and y = 2x − 3 parallel, perpendicular or neither.
① y = 2x + 1 and ② y = 2x − 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: 2.
It is the slope.
b is 1.
m1 = 2
b = 1
2 Slope of ②
m is the number in front of x: 2.
It is the slope.
b is −3.
m2 = 2
b = −3
3 Compare the slopes
Both slopes are 2.
The same steepness.
2 = 2
But they start at different places: 1 and −3.
b = 1 and b = −3
So the lines are parallel: they never meet.
① and ② are parallel
4 Check
Let's see it on the grid.
Draw both lines.
They never meet.
Let's look back.
First: slope of ①.
Then: slope of ②.
Then: compare the slopes.
Last: check.
Answer
① and ② are parallel