Line (0, 1) (2, 5) Step by Step

Step by step

The question

Question: find the equation of the line through (0, 1) and (2, 5).

(0, 1) and (2, 5)

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 (2, 5).

The first point is (0, 1).

m = 5 − 12 − 0

5 minus 1 is 4.

2 minus 0 is 2.

m = 42

4 divided by 2 is 2.

So m = 2.

m = 2

2 Find b

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

Then use the point (0, 1): put x = 0 and y = 1 in.

1 = 2 × 0 + b

2 times 0 is 0.

So b = 1.

1 = b

3 Write the equation

Put m = 2 and b = 1 into y = mx + b.

So the line is y = 2x + 1.

y = 2x + 1

4 Check

Let's check: put x = 0 in.

We get 1, the y of (0, 1).

y = 2(0) + 1 = 0 + 1 = 1

Now x = 2 in.

We get 5, the y of (2, 5).

y = 2(2) + 1 = 4 + 1 = 5

Let's see it.

Both points are on the line y = 2x + 1.

And it crosses the y-axis at 1, just like b says.

Let's look back.

First: find the slope.

Then: find b.

Then: write the equation.

Last: check.

Answer