Write 6x + 3y = 9 as y = mx + b Step by Step

Step by step

The question

Question: write 6x + 3y = 9 as y = mx + b.

6x + 3y = 9

We want y by itself.

Then we can read m and b.

y = mx + b

1 Remove the 6x

We want y by itself.

The 6x is in the way.

To remove 6x, we take away 6x.

We do it on both sides, so they stay equal.

6x + 3y ~~− 6x~~ = 9 − 6x

6x and − 6x make zero.

Cross them out.

Write what is left.

9 and − 6x are not like terms.

They stay as they are.

3y = 9 − 6x

We write the x part first, like in y = mx + b.

Each part keeps its sign.

3y = −6x + 9

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.

3y3 = −6x + 93

3 divided by 3 is 1.

So just y is left.

The 3 divides the whole right side.

So it divides every part: −6x and 9.

Each part keeps its sign on top.

y = −6x3 + 93

Careful!

Divide every part by 3, not only the number.

−6x must be divided by 3 too.

Careful: not y = −6x + 3 ✗

Minus over plus is minus.

−6x divided by 3 is −2x.

−6x3 = −2x

9 divided by 3 is 3.

93 = 3

So y = −2x + 3.

y = −2x + 3

3 Read m and b

m is the number in front of x: −2.

It is the slope.

m = −2

slope

b is the number on its own: 3.

The line crosses the y-axis at 3.

That point is called the y-intercept.

b = 3

crosses the y-axis

4 Check

Let's check with a point.

Put x = 1 into y = −2x + 3.

We get y = 1.

y = −2(1) + 3 = −2 + 3 = 1

Now put x = 1 and y = 1 into 6x + 3y.

6(1) + 3(1) = 6 + 3 = 9

We get 9, the same as the right side.

So the new equation is right!

Let's look back.

First: remove the 6x.

Then: remove the 3.

Then: read m and b.

Last: check.

Answer