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