Question

use the slope formula to find the slope of each line.

1. $overline{lm}$ with $l$ at $(0,2)$ and $m$ at $(2,3)$
2. $overline{jk}$ with $j$ at $(3,3)$ and $k$ at $(4,2)$

tell whether each pair of lines is parallel, perpendicular, or neither.

1. $overline{ef}$ with slope = 3 and $overline{gh}$ with slope = - 1
2. $overline{pq}$ with slope = $\frac{2}{3}$ and $overline{rs}$ with slope = - $\frac{3}{2}$

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Find slope of $\overline{LM}$

For points $L(0,2)$ and $M(2,3)$, let $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(2,3)$. Then $m_{LM}=\frac{3 - 2}{2 - 0}=\frac{1}{2}$.

Step3: Find slope of $\overline{JK}$

For points $J(3,3)$ and $K(4,2)$, let $(x_1,y_1)=(3,3)$ and $(x_2,y_2)=(4,2)$. Then $m_{JK}=\frac{2 - 3}{4 - 3}=- 1$.

Step4: Determine relationship of $\overline{EF}$ and $\overline{GH}$

Two lines are parallel if their slopes are equal and perpendicular if the product of their slopes is - 1. For $\overline{EF}$ with $m_{EF}=3$ and $\overline{GH}$ with $m_{GH}=-1$, since $3
eq - 1$ and $3\times(-1)
eq - 1$, they are neither parallel nor perpendicular.

Step5: Determine relationship of $\overline{PQ}$ and $\overline{RS}$

For $\overline{PQ}$ with $m_{PQ}=\frac{2}{3}$ and $\overline{RS}$ with $m_{RS}=-\frac{3}{2}$, since $\frac{2}{3}\times(-\frac{3}{2})=-1$, they are perpendicular.

Answer:

1. $\frac{1}{2}$
2. $-1$
3. Neither
4. Perpendicular