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:

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 x1 = 1 and y1 = 1.
- The second point is (3, 5), so x2 = 3 and y2 = 5.
3
Substitute x1, y1, x2 and y2 into the formula.
$$Slope = \frac{5 - 1}{3 - 1}$$
$$\:\:\:\:\:\:\:\:\:\:\:\: = \frac{4}{2}$$
$$\:\:\:\:\:\:\:\:\:\:\:\: = 4 \div 2$$
$$\:\:\:\:\:\:\:\:\:\:\:\: = 2$$
Answer:
The slope between the points (1, 1) and (3, 5) is 2.How to Visualize the Slope between Two Points
The slope between the points (1, 1) and (3, 5) is 2. By plotting the points, we can visualize what the slope means.

Positive and Negative Slopes
A positive slope means the line slopes up and to the right:

Zero Slope
A line that goes straight across has zero slope:
Slope of 1
A slope of 1 is a 45° line going from bottom-left to top-right:
Fractional Slope
Slope can be a fraction, such as ½ and ¾. An improper fraction is positive, but less than 1. A slope of 1 gives a 45° line that splits the graph in 2. A fractional slope is less steep than this: