To analyze the initial value and the rate of change based on the provided points \((0.5, 1)\) and \((-1.5, -3)\), we can interpret the points as coordinates in the form \((x, y)\), where \(x\) represents the independent variable and \(y\) represents the dependent variable.
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Initial Value: The initial value is usually taken as the value of \(y\) when \(x\) is at its starting point. In the absence of a clear context (like a time frame), it could refer to the value of \(y\) at the first \(x\) value, which is \(0.5\): \[ \text{Initial value} = y \text{ when } x = 0.5 \quad (y = 1) \] So, the initial value is \(1\).
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Rate of Change: The rate of change can be calculated using the formula for the slope of a line, which is defined as: \[ \text{Rate of change} = \frac{y_2 - y_1}{x_2 - x_1} \] Here, we have two points:
- Point 1: \((x_1, y_1) = (0.5, 1)\)
- Point 2: \((x_2, y_2) = (-1.5, -3)\)
Now we can substitute these values into the formula: \[ \text{Rate of change} = \frac{-3 - 1}{-1.5 - 0.5} = \frac{-4}{-2} = 2 \]
Summary
- Initial Value: \(1\) at \(x = 0.5\)
- Rate of Change: \(2\)
If you meant something different by initial value or rate of change, please provide additional context!
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