Step by step
The question
Question: write x + y = 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.
y is by itself.
2 Read m and b
m is the number in front of x: −1.
It is the slope.
b is the number on its own: 6.
The line crosses the y-axis at 6.
That point is called the y-intercept.
3 Check
Let's check with a point.
Put x = 3 into y = −x + 6.
We get y = 3.
Now put x = 3 and y = 3 into x + y.
We get 6, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the x.
Then: read m and b.
Last: check.