Question

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what is the vertical change from point a to point b? what is the horizontal change from point a to point b? what is the rate of change shown on the graph? give the answer as a decimal rounded to the nearest tenth, if necessary

Explanation:

To solve the problem, we analyze the graph and use the concepts of vertical change, horizontal change, and rate of change (slope).

1. Vertical Change from Point A to Point B

The vertical change (change in \( y \)) is the difference in the \( y \)-coordinates of Points A and B. From the graph, assume Point A has a \( y \)-coordinate of \( y_A \) and Point B has \( y_B \). If the vertical segment (blue dashed line) shows a decrease of 2 units (e.g., \( y_A - y_B = 2 \) or vice versa, but since the line is decreasing, it’s negative), the vertical change is \( -2 \) (or \( 2 \) downward).

2. Horizontal Change from Point A to Point B

The horizontal change (change in \( x \)) is the difference in the \( x \)-coordinates of Points A and B. From the graph, the horizontal segment (blue dashed line) shows an increase of 1 unit (e.g., \( x_B - x_A = 1 \)). Thus, the horizontal change is \( 1 \).

3. Rate of Change (Slope)

The rate of change (slope) is calculated as \( \text{slope} = \frac{\text{vertical change}}{\text{horizontal change}} \).

Substituting the values:
\( \text{slope} = \frac{-2}{1} = -2 \)

Final Answers

• Vertical change: \( \boldsymbol{-2} \) (or \( 2 \) downward, depending on direction)
• Horizontal change: \( \boldsymbol{1} \)
• Rate of change: \( \boldsymbol{-2} \)

Answer:

To solve the problem, we analyze the graph and use the concepts of vertical change, horizontal change, and rate of change (slope).

1. Vertical Change from Point A to Point B

The vertical change (change in \( y \)) is the difference in the \( y \)-coordinates of Points A and B. From the graph, assume Point A has a \( y \)-coordinate of \( y_A \) and Point B has \( y_B \). If the vertical segment (blue dashed line) shows a decrease of 2 units (e.g., \( y_A - y_B = 2 \) or vice versa, but since the line is decreasing, it’s negative), the vertical change is \( -2 \) (or \( 2 \) downward).

2. Horizontal Change from Point A to Point B

The horizontal change (change in \( x \)) is the difference in the \( x \)-coordinates of Points A and B. From the graph, the horizontal segment (blue dashed line) shows an increase of 1 unit (e.g., \( x_B - x_A = 1 \)). Thus, the horizontal change is \( 1 \).

3. Rate of Change (Slope)

The rate of change (slope) is calculated as \( \text{slope} = \frac{\text{vertical change}}{\text{horizontal change}} \).

Substituting the values:
\( \text{slope} = \frac{-2}{1} = -2 \)

Final Answers

• Vertical change: \( \boldsymbol{-2} \) (or \( 2 \) downward, depending on direction)
• Horizontal change: \( \boldsymbol{1} \)
• Rate of change: \( \boldsymbol{-2} \)