Question

2/3 -25 undefined -1/2 3/2 2 1/4 0 -3 3/4

1. slope:
2. slope:
3. slope:
4. slope:
5. slope:
6. slope:

Explanation:

Step1: Recall slope - formula

The slope formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: For graph 7

Choose two points on the line, say $(0, - 3)$ and $(2, - 1)$. Then $x_1 = 0,y_1=-3,x_2 = 2,y_2=-1$. Substitute into the slope - formula: $m=\frac{-1-(-3)}{2 - 0}=\frac{-1 + 3}{2}=\frac{2}{2}=1$.

Step3: For graph 8

Choose two points, say $(0,6)$ and $(8,12)$. Then $x_1 = 0,y_1 = 6,x_2 = 8,y_2 = 12$. Substitute into the slope - formula: $m=\frac{12 - 6}{8 - 0}=\frac{6}{8}=\frac{3}{4}$.

Step4: For graph 9

The line is vertical. For a vertical line, the denominator $x_2 - x_1=0$ in the slope formula. So the slope is undefined.

Step5: For graph 10

Choose two points, say $(0,450)$ and $(10,150)$. Then $x_1 = 0,y_1 = 450,x_2 = 10,y_2 = 150$. Substitute into the slope - formula: $m=\frac{150 - 450}{10 - 0}=\frac{-300}{10}=-30$.

Step6: For graph 11

The line is horizontal. For a horizontal line, $y_2=y_1$, so $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0}{x_2 - x_1}=0$.

Step7: For graph 12

Choose two points, say $(0,16)$ and $(5,2)$. Then $x_1 = 0,y_1 = 16,x_2 = 5,y_2 = 2$. Substitute into the slope - formula: $m=\frac{2 - 16}{5 - 0}=\frac{-14}{5}=- \frac{14}{5}$.

Answer:

1. Slope: $1$
2. Slope: $\frac{3}{4}$
3. Slope: Undefined
4. Slope: $-30$
5. Slope: $0$
6. Slope: $-\frac{14}{5}$