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

Step by step

The question

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

(0, −2) and (1, 1)

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 (1, 1).

The first point is (0, −2).

m = 1 − (−2)1 − 0

Taking away a negative is the same as adding.

− (−) = +

So it becomes (1 + 2)/(1 − 0).

m = 1 + 21 − 0

1 plus 2 is 3.

1 minus 0 is 1.

m = 31

3 divided by 1 is 3.

So m = 3.

m = 3

2 Find b

In y = mx + b, put m = 3.

Then use the point (0, −2): put x = 0 and y = −2 in.

−2 = 3 × 0 + b

3 times 0 is 0.

So b = −2.

−2 = b

3 Write the equation

Put m = 3 and b = −2 into y = mx + b.

So the line is y = 3x − 2.

y = 3x − 2

4 Check

Let's check: put x = 0 in.

We get −2, the y of (0, −2).

y = 3(0) − 2 = 0 − 2 = −2

Now x = 1 in.

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

y = 3(1) − 2 = 3 − 2 = 1

Let's see it.

Both points are on the line y = 3x − 2.

And it crosses the y-axis at −2, just like b says.

Let's look back.

First: find the slope.

Then: find b.

Then: write the equation.

Last: check.

Answer