Write 2x + 3y = 0 as y = mx + b Step by Step

Step by step

The question

Question: write 2x + 3y = 0 as y = mx + b.

2x + 3y = 0

We want y by itself.

Then we can read m and b.

y = mx + b

1 Remove the 2x

We want y by itself.

The 2x is in the way.

To remove 2x, we take away 2x.

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

2x + 3y ~~− 2x~~ = −2x

2x and − 2x make zero.

Cross them out.

0 minus 2x is just −2x.

3y = −2x

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 = −2x3

3 divided by 3 is 1.

So just y is left.

The 3 divides the whole right side.

So it divides every part: −2x.

Each part keeps its sign on top.

y = −2x3

Minus over plus is minus.

−2x/3 is the same as −2/3 times x.

−2x3 = −23x

So y = −(2/3)x.

y = −23x

3 Read m and b

m is the number in front of x: −2/3.

It is the slope.

m = −23

slope

b is the number on its own: 0.

The line crosses the y-axis at 0.

That point is called the y-intercept.

b = 0

crosses the y-axis

4 Check

Let's check with a point.

Put x = −3 into y = −(2/3)x.

We get y = 2.

y = −23(−3) = 2

Now put x = −3 and y = 2 into 2x + 3y.

2(−3) + 3(2) = −6 + 6 = 0

We get 0, the same as the right side.

So the new equation is right!

Let's look back.

First: remove the 2x.

Then: remove the 3.

Then: read m and b.

Last: check.

Answer