Step by step
The question
Question: are y = 3x + 2 and 6x − 2y = −4 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: 3.
It is the slope.
b is 2.
2 Slope of ②
② is not y = mx + b yet.
So we write it as y = mx + b first.
We want y by itself.
The 6x is in the way.
To remove 6x, we take away 6x.
We do it on both sides, so they stay equal.
6x and − 6x make zero.
Cross them out.
Write what is left.
We write the x part first, like in y = mx + b.
Each part keeps its sign.
−2y means −2 times y.
We want just y.
To remove times −2, we divide by −2.
We do it on both sides, so they stay equal.
−2 divided by −2 is 1.
So just y is left.
The −2 divides the whole right side.
So it divides every part: −6x and −4.
Each part keeps its sign on top.
Minus over minus is plus.
−6x divided by −2 is 3x.
Minus over minus is plus.
−4 divided by −2 is 2.
So y = 3x + 2.
m is the number in front of x: 3.
It is the slope.
3 Compare the slopes
Both slopes are 3.
The same steepness.
And both have b = 2.
They start at the same place too.
Careful!
Same slope and same b is one line drawn twice.
Parallel lines must start at different places.
So it is the same line: every point is on both.
4 Check
Let's see it on the grid.
Draw both lines.
One line on top of the other.
Let's look back.
First: slope of ①.
Then: slope of ②.
Then: compare the slopes.
Last: check.