Step by step
The question
Question: are y = (1/2)x + 3 and x − 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: 1/2.
It is the slope.
b is 3.
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 x is in the way.
To remove x, we take away x.
We do it on both sides, so they stay equal.
x and − x 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: −x and 4.
Each part keeps its sign on top.
Minus over minus is plus.
−x over −2 is the same as 1/2 times x.
Plus over minus is minus.
4 divided by −2 is −2.
So y = (1/2)x − 2.
m is the number in front of x: 1/2.
It is the slope.
3 Compare the slopes
Both slopes are 1/2.
The same steepness.
But they start at different places: 3 and −2.
So the lines are parallel: they never meet.
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.