Equation of a Line Between Two Points
What Is the Equation of a Line Between Points?
A linear equation is an equation that represents a line.
If we are given two points, we can draw a line between them.
If we know the Cartesian coordinates of the two points, then we can find the equation of the line.
The image below shows what we mean by two points (x_{1}, y_{1}) and (x_{2}, y_{2}) being joined by a line:
The equation of the line between the points is given by the formula:

y and x are the Cartesian coordinates of points on the line.

(x_{1}, y_{1}) and (x_{2}, y_{2}) are two points on the line.
How to Find the Equation of a Line Between Two Points
Finding the equation of a line between two points is easy.
Question
What is the equation of the line that passes through the points (1, 2) and (4, 8)?
StepbyStep:
1
Start with the formula:
$$y  y_1 = \frac{y_2  y_1}{x_2  x_1}(x  x_1)$$
2
Find the Cartesian coordinates of the points. In our example:

The first point is (1, 2), so x_{1} = 1 and y_{1} = 2.

The second point is (4, 8), so x_{2} = 4 and y_{2} = 8.
3
Substitute x_{1}, y_{1}, x_{2} and y_{2} into the formula.
$$y  2 = \frac{8  2}{4  1}(x  1)$$
4
Tidy up the equation.
$$y  2 = \frac{6}{3}(x  1)$$ $$y  2 = 2(x  1)$$
Answer:
The equation of the line between the points (1, 2) and (4, 8) is y − 2 = 2(x − 1).