Line (0, 0) (3, 6) Step by Step

Step by step

The question

Question: find the equation of the line through (0, 0) and (3, 6).

(0, 0) and (3, 6)

Every line that is not straight up and down is y = mx + b.

m is the slope.

b is where the line crosses the y-axis: where we start.

So we need m and b.

y = mx + b

m = slope

b = start

1 Find the slope

We call the slope m.

m = rise over run.

m = riserun

The top is the change in y: second y minus first y.

The bottom is the change in x: second x minus first x.

m = y₂ − y₁x₂ − x₁

Put the numbers in.

The second point is (3, 6).

The first point is (0, 0).

m = 6 − 03 − 0

6 minus 0 is 6.

3 minus 0 is 3.

m = 63

6 divided by 3 is 2.

So m = 2.

m = 2

2 Find b

In y = mx + b, put m = 2.

Then use the point (0, 0): put x = 0 and y = 0 in.

0 = 2 × 0 + b

2 times 0 is 0.

So b = 0.

0 = b

3 Write the equation

Put m = 2 and b = 0 into y = mx + b.

So the line is y = 2x.

y = 2x

4 Check

Let's check: put x = 0 in.

We get 0, the y of (0, 0).

y = 2(0) = 0

Now x = 3 in.

We get 6, the y of (3, 6).

y = 2(3) = 6

Let's see it.

Both points are on the line y = 2x.

And it crosses the y-axis at 0, just like b says.

Let's look back.

First: find the slope.

Then: find b.

Then: write the equation.

Last: check.

Answer