Step by step
The question
Question: write x − 3y = 6 as y = mx + b.
We want y by itself.
Then we can read m and b.
1 Remove the x
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.
6 and − x 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: −x and 6.
Each part keeps its sign on top.
Careful!
Divide every part by −3, not only the number.
−x must be divided by −3 too.
Minus over minus is plus.
−x over −3 is the same as 1/3 times x.
Plus over minus is minus.
6 divided by −3 is −2.
So y = (1/3)x − 2.
3 Read m and b
m is the number in front of x: 1/3.
It is the slope.
b is the number on its own: −2.
The line crosses the y-axis at −2.
That point is called the y-intercept.
4 Check
Let's check with a point.
Put x = 3 into y = (1/3)x − 2.
We get y = −1.
Now put x = 3 and y = −1 into x − 3y.
We get 6, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the x.
Then: remove the −3.
Then: read m and b.
Last: check.