Algebra 1 / Unit 5: Linear Functions
5.1 Slope and Rate of Change
Notes
Slope measures steepness: $\displaystyle m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$.
- Positive slope rises left to right; negative slope falls; zero slope is a horizontal line; a vertical line has undefined slope.
- In context, slope is a rate of change with units, like dollars per hour.
Practice
Find the slope through $(2, 5)$ and $(6, 13)$.
$\displaystyle \frac{13 - 5}{6 - 2} = \frac{8}{4}$.
Find the slope through $(-1, 4)$ and $(3, -4)$.
$\displaystyle \frac{-4 - 4}{3 - (-1)} = \frac{-8}{4}$.
The line through $(5, 2)$ and $(5, 9)$ has slope:
The run is $5 - 5 = 0$, and you can't divide by 0. It is a vertical line.
Ready for more? Take the Unit 5 test.