Study Guide: 8-5-7. Parallel and Perpendicular Lines
Vocabulary
| Term | Description |
|---|---|
| Cartesian Plane | a two-dimensional plane divided into four quadrants using x- and y-axis |
| Slope | a ratio of the rate at which the dependent variable is changing versus the rate at which the independent variable is changing; frequently expressed as $\frac{RISE}{RUN}$, or $\frac{\textit{The change in y}}{\textit{The change in x}}$ |
| Parallel Lines | lines having the same slope and different y-intercepts. |
| Perpendicular Lines | lines having oposite and inverse slopes. |
| Oposite Number | numbers that are the exact same distance from zero, but on opposite sides of zero, such as $2$ and $-2$. |
| Inverse Number | numbers that when multiplied together equal 1, such as $ \frac{2}{1} \times \frac{1}{2} = 1$. Also called reciprocals. |
Parallel Lines
Lines that are parallel have the same slope and different y-intercepts.
The following equations are parallel. Plot them on a grid to see.
\begin{align} y &= 3x + 4 \\\ y &= 3x \\\ y &= 3x - 6 \end{align}
Perpendicular Lines
Lines that are perpendicular meet at 90 degree angles. Their slopes are always opposite and inverse.
The following equations are perpendicular. Plot them on a grid to see.
\begin{align} y &= 3x + 4 \\\ y &= -\frac{1}{3}x \end{align}
Source: https://class.ronliskey.com/study/mathematics-8/8-5-7-parallel-perpendicular-lines/