To find the initial value and the rate of change between the points (0, 0) and (2, 3), we can consider these points in the context of a linear relationship.
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Initial Value: This is the value of the function when \( x = 0 \). From the point (0, 0), we see that when \( x = 0 \), \( y = 0 \). Therefore, the initial value is 0.
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Rate of Change (Slope): The rate of change can be calculated using the formula for the slope of a line, which is given by:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points \( (0, 0) \) and \( (2, 3) \):
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (2, 3) \)
Plugging in the values:
\[ \text{slope} = \frac{3 - 0}{2 - 0} = \frac{3}{2} \]
So, the initial value is 0, and the rate of change (slope) is \(\frac{3}{2}\).