Question

estimate the slope of the line.

Explanation:

Step1: Recall slope formula

The slope $m$ of a line is given by $m=\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: For the first graph

Choose two points, say $(0,1)$ and $(1,3)$. Then $m=\frac{3 - 1}{1 - 0}=\frac{2}{1}=2$.

Step3: For the second graph

The line is vertical. For a vertical line, the change in $x$ ($\Delta x$) is 0. The slope formula $\frac{\Delta y}{\Delta x}$ is undefined when $\Delta x = 0$. So the slope is undefined.

Step4: For the third graph

Choose two points, say $(0,1)$ and $(1,0)$. Then $m=\frac{0 - 1}{1 - 0}=\frac{-1}{1}=- 1$.

Answer:

1. 2
2. Undefined
3. -1