The Lesson
The slope (or gradient) between two points measures the steepness of the line joining the points.The Theory
The slope between two points can be found using the formula below:In the formula, (x_{1}, y_{1}) and (x_{2}, y_{2}) are the Cartesian coordinates of the two points. The image below shows what we mean by the slope between the two points:Note: (x_{1}, y_{1}) is the point on the left and (x_{2}, y_{2}) is the point on the right.How to Find the Slope Between Two Points
Finding the slope between two points is easy.Question
What is the slope between the points (1, 1) and (3, 5)?Step-by-Step:
1
Start with the formula.:
$$Slope = \frac{y_2 - y_1}{x_2 - x_1}$$
Don't forget: / means ÷
2
Find the Cartesian coordinates of the points. In our example:
- The first point is (1, 1), so x_{1} = 1 and y_{1} = 1.
- The second point is (3, 5), so x_{2} = 3 and y_{2} = 5.
3
Substitute x_{1}, y_{1}, x_{2} and y_{2} into the formula.
$$Slope = \frac{5 - 1}{3 - 1}$$
$$\:\:\:\:\:\:\:\:\:\:\:\: = \frac{4}{2}$$
$$\:\:\:\:\:\:\:\:\:\:\:\: = 4 \div 2$$
$$\:\:\:\:\:\:\:\:\:\:\:\: = 2$$