Step by step
The question
Question: write 3x + 4y = 8 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.
8 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.
2 Remove the 4
4y means 4 times y.
We want just y.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just y is left.
The 4 divides the whole right side.
So it divides every part: −3x and 8.
Each part keeps its sign on top.
Careful!
Divide every part by 4, not only the number.
−3x must be divided by 4 too.
Minus over plus is minus.
−3x/4 is the same as −3/4 times x.
8 divided by 4 is 2.
So y = −(3/4)x + 2.
3 Read m and b
m is the number in front of x: −3/4.
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 = 4 into y = −(3/4)x + 2.
We get y = −1.
Now put x = 4 and y = −1 into 3x + 4y.
We get 8, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the 3x.
Then: remove the 4.
Then: read m and b.
Last: check.