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

Step by step

The question

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

(0, 3) and (3, 0)

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, 0).

The first point is (0, 3).

m = 0 − 33 − 0

0 minus 3 is −3.

3 minus 0 is 3.

m = −33

−3 divided by 3 is −1.

So m = −1.

m = −1

2 Find b

In y = mx + b, put m = −1.

Then use the point (0, 3): put x = 0 and y = 3 in.

3 = −1 × 0 + b

−1 times 0 is 0.

So b = 3.

3 = b

3 Write the equation

Put m = −1 and b = 3 into y = mx + b.

So the line is y = −x + 3.

y = −x + 3

4 Check

Let's check: put x = 0 in.

We get 3, the y of (0, 3).

y = −(0) + 3 = 0 + 3 = 3

Now x = 3 in.

We get 0, the y of (3, 0).

y = −3 + 3 = 0

Let's see it.

Both points are on the line y = −x + 3.

And it crosses the y-axis at 3, just like b says.

Let's look back.

First: find the slope.

Then: find b.

Then: write the equation.

Last: check.

Answer