To find the initial value and the rate of change of the linear function represented by the points (0, 0) and (2, 3), we can follow these steps:
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Initial Value: The initial value of a linear function is the y-value when x = 0. From the point (0, 0), we see that the initial value is: \[ \text{Initial value} = 0 \]
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Rate of Change (slope): The rate of change (slope) can be calculated using the formula: \[ \text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 0) and (2, 3):
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (2, 3) \)
Plugging in these values: \[ \text{slope} = \frac{3 - 0}{2 - 0} = \frac{3}{2} \]
Thus, the initial value is \(0\) and the rate of change is \(\frac{3}{2}\).
In summary:
- Initial value: 0
- Rate of change: \(\frac{3}{2}\)
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