Question

m = \frac{rise}{run} = \underline{\quad\quad}

m = \frac{rise}{run} = \underline{\quad\quad}

m =

m =

Explanation:

Step1: First Graph (Leftmost)

To find the slope \( m = \frac{\text{rise}}{\text{run}} \), we identify two points on the line. Let's take the point where it crosses the y - axis (0, -1) and another point, say (2, 1). The rise is \( 1 - (-1)=2 \) and the run is \( 2 - 0 = 2 \). So \( m=\frac{2}{2}=1 \).

Step2: Second Graph

For the second graph, let's take two points. Let's say the line passes through (0, 3) and (2, -3). The rise is \( - 3-3=-6 \) and the run is \( 2 - 0=2 \). So \( m=\frac{-6}{2}=-3 \).

Step3: Third Graph

A horizontal line has a slope of 0 because the rise (change in y - value) is 0 for any run (change in x - value). So \( m = 0 \).

Step4: Fourth Graph

A vertical line has an undefined slope because the run (change in x - value) is 0 (since x is constant for all y), and division by zero is undefined. So \( m=\text{undefined} \).

Answer:

First graph: \( m=\frac{2}{2} = 1 \)

Second graph: \( m=\frac{-6}{2}=-3 \)

Third graph: \( m = 0 \)

Fourth graph: \( m=\text{undefined} \)