Slope and y-intercept of 5x - 2y = 10 Step by Step

Step by step

The question

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

5x − 2y = 10

We want y by itself.

Then we can read m and b.

y = mx + b

1 Remove the 5x

We want y by itself.

The 5x is in the way.

To remove 5x, we take away 5x.

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

5x − 2y ~~− 5x~~ = 10 − 5x

5x and − 5x make zero.

Cross them out.

Write what is left.

10 and − 5x are not like terms.

They stay as they are.

−2y = 10 − 5x

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

Each part keeps its sign.

−2y = −5x + 10

2 Remove the −2

−2y means −2 times y.

We want just y.

To remove times −2, we divide by −2.

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

−2y−2 = −5x + 10−2

−2 divided by −2 is 1.

So just y is left.

The −2 divides the whole right side.

So it divides every part: −5x and 10.

Each part keeps its sign on top.

y = −5x−2 + 10−2

Careful!

Divide every part by −2, not only the number.

−5x must be divided by −2 too.

Careful: not y = −5x − 5 ✗

Minus over minus is plus.

−5x over −2 is the same as 5/2 times x.

−5x−2 = 52x

Plus over minus is minus.

10 divided by −2 is −5.

10−2 = −5

So y = (5/2)x − 5.

y = 52x − 5

3 Read m and b

m is the number in front of x: 5/2.

It is the slope.

m = 52

slope

b is the number on its own: −5.

The line crosses the y-axis at −5.

That point is called the y-intercept.

b = −5

crosses the y-axis

4 Check

Let's check with a point.

Put x = 4 into y = (5/2)x − 5.

We get y = 5.

y = 52(4) − 5 = 10 − 5 = 5

Now put x = 4 and y = 5 into 5x − 2y.

5(4) − 2(5) = 20 − 10 = 10

We get 10, the same as the right side.

So the new equation is right!

Let's look back.

First: remove the 5x.

Then: remove the −2.

Then: read m and b.

Last: check.

Answer