Write 2x + 5y = 10 as y = mx + b Step by Step

Step by step

The question

Question: write 2x + 5y = 10 as y = mx + b.

2x + 5y = 10

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 + 5y ~~− 2x~~ = 10 − 2x

2x and − 2x make zero.

Cross them out.

Write what is left.

10 and − 2x are not like terms.

They stay as they are.

5y = 10 − 2x

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

Each part keeps its sign.

5y = −2x + 10

2 Remove the 5

5y means 5 times y.

We want just y.

To remove times 5, we divide by 5.

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

5y5 = −2x + 105

5 divided by 5 is 1.

So just y is left.

The 5 divides the whole right side.

So it divides every part: −2x and 10.

Each part keeps its sign on top.

y = −2x5 + 105

Careful!

Divide every part by 5, not only the number.

−2x must be divided by 5 too.

Careful: not y = −2x + 2 ✗

Minus over plus is minus.

−2x/5 is the same as −2/5 times x.

−2x5 = −25x

10 divided by 5 is 2.

105 = 2

So y = −(2/5)x + 2.

y = −25x + 2

3 Read m and b

m is the number in front of x: −2/5.

It is the slope.

m = −25

slope

b is the number on its own: 2.

The line crosses the y-axis at 2.

That point is called the y-intercept.

b = 2

crosses the y-axis

4 Check

Let's check with a point.

Put x = −5 into y = −(2/5)x + 2.

We get y = 4.

y = −25(−5) + 2 = 2 + 2 = 4

Now put x = −5 and y = 4 into 2x + 5y.

2(−5) + 5(4) = −10 + 20 = 10

We get 10, the same as the right side.

So the new equation is right!

Let's look back.

First: remove the 2x.

Then: remove the 5.

Then: read m and b.

Last: check.

Answer