Question

find the slope of each line. (example 2)
2.
3.

Explanation:

Problem 2:

Step1: Identify two points on the line

Let's take two clear points on the blue line. From the graph, we can see that when \( x = 1 \), \( y = 0 \) (one point: \( (1, 0) \)) and when \( x = 3 \), \( y=- 2 \) (another point: \( (3,-2) \)). Or we can use the grid to find the rise and run. The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \) or \( m=\frac{\text{rise}}{\text{run}} \). Looking at the red and blue right triangle, the run (horizontal change) is \( 2 \) units (from \( x = 1 \) to \( x = 3 \), change in \( x \) is \( 3 - 1=2 \)) and the rise (vertical change) is \( - 2 \) units (from \( y = 0 \) to \( y=-2 \), change in \( y \) is \( - 2-0=-2 \)).

Step2: Calculate the slope

Using the slope formula \( m = \frac{\text{rise}}{\text{run}} \), we have \( m=\frac{- 2}{2}=-1 \).

Problem 3:

Step1: Identify two points on the line

From the graph, let's take two points. When \( x = 1 \), \( y = 1 \) (one point: \( (1, 1) \)) and when \( x=-3 \), \( y = - 3 \) (another point: \( (-3,-3) \)). Or using the grid, the run (horizontal change) between two points: from \( x=-3 \) to \( x = 1 \), change in \( x \) is \( 1-(-3)=4 \). The rise (vertical change) from \( y=-3 \) to \( y = 1 \), change in \( y \) is \( 1-(-3)=4 \).

Step2: Calculate the slope

Using the slope formula \( m=\frac{\text{rise}}{\text{run}} \), we have \( m = \frac{4}{4}=1 \).

Problem 2 Answer: \(-1\)

Problem 3 Answer: \(1\)

Answer:

Step1: Identify two points on the line

From the graph, let's take two points. When \( x = 1 \), \( y = 1 \) (one point: \( (1, 1) \)) and when \( x=-3 \), \( y = - 3 \) (another point: \( (-3,-3) \)). Or using the grid, the run (horizontal change) between two points: from \( x=-3 \) to \( x = 1 \), change in \( x \) is \( 1-(-3)=4 \). The rise (vertical change) from \( y=-3 \) to \( y = 1 \), change in \( y \) is \( 1-(-3)=4 \).

Step2: Calculate the slope

Using the slope formula \( m=\frac{\text{rise}}{\text{run}} \), we have \( m = \frac{4}{4}=1 \).

Problem 2 Answer: \(-1\)

Problem 3 Answer: \(1\)