Integrated Math 1 / Unit 4: Linear Functions and Arithmetic Sequences
4.1 Slope and Rate of Change
Notes
The slope of a line is its steepness: $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}}$.
- Positive slope rises left to right; negative slope falls.
- A horizontal line has slope 0. A vertical line has undefined slope.
- In context, slope is a constant rate of change, like dollars per hour.
- Example: through $(2, 3)$ and $(6, 11)$: $\displaystyle m = \frac{11 - 3}{6 - 2} = 2$.
Practice
What is the slope of the line through $(2, 3)$ and $(6, 11)$?
$\displaystyle \frac{11 - 3}{6 - 2} = \frac{8}{4} = 2$.
What is the slope of the line through $(-1, 5)$ and $(3, -3)$?
$\displaystyle \frac{-3 - 5}{3 - (-1)} = \frac{-8}{4} = -2$.
What is the slope of the line $x = 4$?
A vertical line has no run (change in $x$ is 0), so its slope is undefined.
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