Find the equation of the straight line through (0, 1) and (2, 7)… Step by Step

Step by step

The question

Question: find the equation of the line through (0, 1) and (2, 7).

(0, 1) and (2, 7)

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.

So we need m and b.

y = mx + b

m = slope

b = crosses the y-axis

1 Find the slope

We find the slope m with the slope formula.

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, 7).

The first point is (0, 1).

m = 7 − 12 − 0

7 minus 1 is 6.

2 minus 0 is 2.

m = 62

6 divided by 2 is 3.

So m = 3.

m = 3

2 Find b

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

We can use either point.

(0, 1) is easier: its x is 0.

The point (0, 1) is on the line, so its x and y fit.

We put x = 0 and y = 1 in.

1 = 3 × 0 + b

3 times 0 is 0.

0 plus b is just b.

So b = 1.

1 = b

3 Write the equation

Put m = 3 and b = 1 into y = mx + b.

So the line is y = 3x + 1.

y = 3x + 1

4 Check

Let's check: put x = 0 in.

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

y = 3(0) + 1 = 0 + 1 = 1

Now put x = 2 in.

We get 7, the y of (2, 7).

y = 3(2) + 1 = 6 + 1 = 7

Let's see both points on the grid.

Both are on the line y = 3x + 1.

Go right 1,

up 3: the slope is 3.

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