Geometry / Unit 3: Parallel and Perpendicular Lines
3.5 Slopes of Parallel and Perpendicular Lines
Notes
Slope measures steepness: $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$ (rise over run).
- Parallel lines have equal slopes.
- Perpendicular lines have slopes that are opposite reciprocals: their product is $-1$.
- Horizontal lines (slope 0) are perpendicular to vertical lines (undefined slope).
- Example: a line with slope $\displaystyle \frac{2}{3}$ is perpendicular to a line with slope $\displaystyle -\frac{3}{2}$.
Practice
What is the slope of the line through $(2, 1)$ and $(6, 9)$?
$\displaystyle \frac{9 - 1}{6 - 2} = \frac{8}{4} = 2$.
A line has slope $\displaystyle -\frac{4}{5}$. What is the slope of a line perpendicular to it?
Take the reciprocal and change the sign.
Which line is parallel to $y = 3x - 7$?
Parallel lines have the same slope, 3.
Ready for more? Take the Unit 3 test.