Step by step
The question
Question: write 3x − 3y = 9 as y = mx + b.
We want y by itself.
Then we can read m and b.
1 Remove the 3x
We want y by itself.
The 3x is in the way.
To remove 3x, we take away 3x.
We do it on both sides, so they stay equal.
3x and − 3x make zero.
Cross them out.
Write what is left.
9 and − 3x are not like terms.
They stay as they are.
We write the x part first, like in y = mx + b.
Each part keeps its sign.
2 Remove the −3
−3y means −3 times y.
We want just y.
To remove times −3, we divide by −3.
We do it on both sides, so they stay equal.
−3 divided by −3 is 1.
So just y is left.
The −3 divides the whole right side.
So it divides every part: −3x and 9.
Each part keeps its sign on top.
Careful!
Divide every part by −3, not only the number.
−3x must be divided by −3 too.
Minus over minus is plus.
−3x divided by −3 is x.
Plus over minus is minus.
9 divided by −3 is −3.
So y = x − 3.
3 Read m and b
m is the number in front of x: 1.
It is the slope.
b is the number on its own: −3.
The line crosses the y-axis at −3.
That point is called the y-intercept.
4 Check
Let's check with a point.
Put x = 1 into y = x − 3.
We get y = −2.
Now put x = 1 and y = −2 into 3x − 3y.
We get 9, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the 3x.
Then: remove the −3.
Then: read m and b.
Last: check.