Step by step
The question
Question: write 3x + y = 7 as y = mx + b.
We want y by itself.
Then we can read m and b.
1 Remove the 3x
We want y by itself.
The 3x is in the way.
To remove 3x, we take away 3x.
We do it on both sides, so they stay equal.
3x and − 3x make zero.
Cross them out.
Write what is left.
7 and − 3x 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: −3.
It is the slope.
b is the number on its own: 7.
The line crosses the y-axis at 7.
That point is called the y-intercept.
3 Check
Let's check with a point.
Put x = 2 into y = −3x + 7.
We get y = 1.
Now put x = 2 and y = 1 into 3x + y.
We get 7, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the 3x.
Then: read m and b.
Last: check.