To determine the initial value and the rate of change of a linear function from a graph, you would typically follow these steps:
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Identify the Initial Value: The initial value of a linear function is the y-intercept, which is the point where the graph crosses the y-axis. Look for the point on the y-axis (where \(x = 0\)) to find this value.
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Determine the Rate of Change (Slope): The rate of change (or slope) of a linear function indicates how much \(y\) changes for a one-unit increase in \(x\). To find this:
- Select two points on the line. Let’s call them \((x_1, y_1)\) and \((x_2, y_2)\).
- Use the slope formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
If you have specific coordinates from the graph, I can help calculate the slope and identify the initial value. However, if you don’t have specific values or a graph provided, I would recommend using the steps above to find them yourself. If you can describe the graph or provide details, I can assist further!