To determine the initial value and the rate of change of the linear function based on the points you've provided, we can use the coordinates of the points:
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Initial Value: The initial value of a linear function (often referred to as the y-intercept) occurs when \( x = 0 \). From the points given, we see that at \( (0, 1) \), the value of the function is 1. Therefore, the initial value is 1.
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Rate of Change: The rate of change (or slope) of the linear function can be calculated using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Let's use two of the points, for example, \( (-3, 2.5) \) and \( (0, 1) \):
- \( y_2 = 1 \), \( y_1 = 2.5 \)
- \( x_2 = 0 \), \( x_1 = -3 \)
Plugging in these values gives us: \[ \text{slope} = \frac{1 - 2.5}{0 - (-3)} = \frac{-1.5}{3} = -0.5 \]
Thus, the rate of change is -0.5.
To summarize:
- The initial value is 1
- The rate of change is -0.5
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