To determine the initial value and the rate of change of a linear function given a graph, you typically need to analyze the graph visually. However, since I cannot see the graph directly, I can guide you through the process to find these values.
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Initial Value: This is the value of the function when the independent variable (often represented as \(x\)) is equal to zero. To find the initial value:
- Look for the point where the line crosses the y-axis. This point gives you the initial value.
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Rate of Change: The rate of change refers to the slope of the line. To determine the slope:
- Identify two points on the line, preferably far apart to minimize error. Let's say you have two points, \( (x_1, y_1) \) and \( (x_2, y_2) \).
- Use the formula for slope (rate of change): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
- Calculate this value and round it to three decimal places.
If you give me the coordinates of two points on the graph or the y-intercept, I can assist you further in calculating these values.