Step by step
The question
Question: are y = 2x + 3 and y = (1/2)x − 1 parallel, perpendicular or neither.
The slopes tell us which.
Same slope: parallel.
Flip the slope and change its sign: perpendicular.
1 Slope of ①
m is the number in front of x: 2.
It is the slope.
b is 3.
2 Slope of ②
m is the number in front of x: 1/2.
It is the slope.
b is −1.
3 Compare the slopes
2 and 1/2 are not the same.
So the lines are not parallel.
2 is 2/1.
Flip it: 1/2.
Then change the sign: −1/2.
We get −1/2.
The second slope is 1/2.
Not the same.
Careful!
Flipped, but the sign did not change.
For a square corner, the sign must change too.
So they are neither parallel nor perpendicular.
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.