Calculate the slope between two points

Slope describes the constant rate of change between two points, found as the change in $y$ divided by the change in $x$ : $m=(y_2-y_1)/(x_2-x_1)$ . Learners interpret slope as rise over run and connect its sign and value to a line’s direction and steepness, recognizing zero slope for horizontal lines and an undefined slope for vertical lines; calculus-based rates and more advanced generalizations are not included.

Detailed Explanation: Calculate the slope between two points

Slope tells how much a line rises or falls compared with how far it moves left or right.

Use the formula

m=\frac{y_2-y_1}{x_2-x_1}

where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.

Example

Find the slope of the line through $(2,3)$ and $(6,11)$ .

Step 1: Identify the coordinates.

Let

(x_1,y_1)=(2,3), \qquad (x_2,y_2)=(6,11)

Step 2: Substitute into the formula.

m=\frac{11-3}{6-2}

Step 3: Simplify.

m=\frac{8}{4}=2

The slope is

\boxed{2}

This means the line rises $2$ units for every $1$ unit it moves to the right. A positive slope means the line goes upward from left to right. A negative slope means it goes downward. A horizontal line has slope $0$ , while a vertical line has an undefined slope because its change in $x$ is $0$ .

Learn by doing: Calculate the slope between two points

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Slope of a Line from Coordinates of Points

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