Step by step
The question
Question: write 4x − 2y = 6 as y = mx + b.
We want y by itself.
Then we can read m and b.
1 Remove the 4x
We want y by itself.
The 4x is in the way.
To remove 4x, we take away 4x.
We do it on both sides, so they stay equal.
4x and − 4x make zero.
Cross them out.
Write what is left.
6 and − 4x 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 −2
−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: −4x and 6.
Each part keeps its sign on top.
Careful!
Divide every part by −2, not only the number.
−4x must be divided by −2 too.
Minus over minus is plus.
−4x divided by −2 is 2x.
Plus over minus is minus.
6 divided by −2 is −3.
So y = 2x − 3.
3 Read m and b
m is the number in front of x: 2.
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 = 2x − 3.
We get y = −1.
Now put x = 1 and y = −1 into 4x − 2y.
We get 6, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the 4x.
Then: remove the −2.
Then: read m and b.
Last: check.