Step by step
The question
Question: find the equation of the line through (−1, 3) and (2, 3).
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.
1 Find the slope
We call the slope m.
m = rise over run.
The top is the change in y: second y minus first y.
The bottom is the change in x: second x minus first x.
Put the numbers in.
The second point is (2, 3).
The first point is (−1, 3).
Taking away a negative is the same as adding.
So it becomes (3 − 3)/(2 + 1).
3 minus 3 is 0.
2 plus 1 is 3.
0 divided by 3 is 0.
So m = 0.
2 Find b
m is 0, so there is no x term: y = b.
Use the point (−1, 3): put y = 3 in.
So b = 3.
3 Write the equation
Put m = 0 and b = 3 into y = mx + b.
So the line is y = 3.
4 Check
Let's check: put x = −1 in.
We get 3, the y of (−1, 3).
Now x = 2 in.
We get 3, the y of (2, 3).
Let's see it.
Both points are on the line y = 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.