Lesson 7: Analyze Linear Equations: y = mx

Property

The slope of the line between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

Examples

• Find the slope between $(2, 3)$ and $(7, 9)$. Using the formula: $m = \frac{9 - 3}{7 - 2} = \frac{6}{5}$.
• Find the slope between $(-1, 5)$ and $(3, -3)$. Using the formula: $m = \frac{-3 - 5}{3 - (-1)} = \frac{-8}{4} = -2$.
• Find the slope between $(-4, -2)$ and $(-6, 8)$. Using the formula: $m = \frac{8 - (-2)}{-6 - (-4)} = \frac{10}{-2} = -5$.

Explanation

The slope formula is a way to calculate rise over run without a graph. It finds the vertical distance between points $(y_2 - y_1)$ and divides it by the horizontal distance $(x_2 - x_1)$ to find the steepness.

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.