Slope

The slope is the inclination of a line with respect to the x-axis.

It is denoted by the letter m.

Slope of a Line

Slope given two points:

Slope Given Two Points

Slope given the angle:

Slope Given the Angle

Slope given a vector of the line:

Slope Given a Vector of the Line

Slope given the equation of the line:

Slope Given the Equation of the Line

Two lines are parallel if their slopes are equal.

Equal Slopes

Two lines are perpendicular if their slopes are the inverse of each other and their signs are opposite.

Inverse Slopes

Examples

The slope of the line through the points A = (2, 1) and B = (4, 7) is:

Slope of a Line Example

The line passes through Points A = (1, 2) and B = (1, 7) and has no slope since division by 0 is undefined.

Slope of a Line Example

Slope of a Line

If the angle between the line with the positive x-axis is acute, the slope is positive and grows as the angle increases.

Slope of a Line

If the angle between the line with the positive x-axis is obtuse, the slope is negative and decreases as the angle increases.