Question

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

1. $overline{ab}$
2. $overline{cd}$
3. $overline{ef}$
4. $overline{gh}$

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 $\overline{AB}$

Let $A=(-2, - 2)$ and $B=(2,-2)$. Then $x_1=-2,y_1 = - 2,x_2=2,y_2=-2$. Substitute into the slope formula: $m=\frac{-2-(-2)}{2 - (-2)}=\frac{-2 + 2}{2+2}=\frac{0}{4}=0$.

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

Let $C=(4,-2)$ and $D=(-2,3)$. Then $x_1 = 4,y_1=-2,x_2=-2,y_2 = 3$. Substitute into the slope formula: $m=\frac{3-(-2)}{-2 - 4}=\frac{3 + 2}{-6}=-\frac{5}{6}$.

Step4: Find slope of $\overline{EF}$

Let $E=(3,-1)$ and $F=(6,3)$. Then $x_1 = 3,y_1=-1,x_2=6,y_2 = 3$. Substitute into the slope formula: $m=\frac{3-(-1)}{6 - 3}=\frac{3 + 1}{3}=\frac{4}{3}$.

Step5: Find slope of $\overline{GH}$

Let $G=(-2,1)$ and $H=(-2,3)$. Then $x_1=-2,y_1 = 1,x_2=-2,y_2 = 3$. Substitute into the slope formula: $m=\frac{3 - 1}{-2-(-2)}=\frac{2}{0}$, which is undefined since division by zero is not allowed.

Answer:

1. $0$
2. $-\frac{5}{6}$
3. $\frac{4}{3}$
4. Undefined