Step by step
The question
Question: write x + 2y = 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 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: −x and 6.
Each part keeps its sign on top.
Careful!
Divide every part by 2, not only the number.
−x must be divided by 2 too.
Minus over plus is minus.
−x/2 is the same as −1/2 times x.
6 divided by 2 is 3.
So y = −(1/2)x + 3.
3 Read m and b
m is the number in front of x: −1/2.
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 = 2 into y = −(1/2)x + 3.
We get y = 2.
Now put x = 2 and y = 2 into x + 2y.
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 2.
Then: read m and b.
Last: check.