Lesson 2: Slope of a Line

Property

Given two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ on a line, the slope $m$ of the line is calculated using the formula:

Examples

Property

Positive slopes correspond to lines that increase from left to right.
Negative slopes correspond to lines that decrease from left to right.
The larger the absolute value of the slope, the steeper the graph.

Examples

• A line with slope $m = 2$ is steeper than a line with slope $m = \frac{1}{3}$ because $|2| > |\frac{1}{3}|$.

• A line with slope $m = -3$ is steeper than a line with slope $m = -1$ because $|-3| > |-1|$. Both lines slant downwards.

Property

• The slope of a horizontal line, $y=b$, is 0.
• The slope of a vertical line, $x=a$, is undefined.

Examples

• The slope of the horizontal line $y = 6$ is $m=0$.
• The slope of the vertical line $x = -2$ is undefined.
• The slope between points $(5, -1)$ and $(-3, -1)$ is $m = \frac{-1 - (-1)}{-3 - 5} = \frac{0}{-8} = 0$. The line is horizontal.

Explanation

A horizontal line is perfectly flat, so its 'rise' is always 0, making the slope 0. A vertical line is perfectly steep, so its 'run' is 0. Since we can't divide by zero, the slope is called undefined.