Question

intial value and rate of change

(0.5, 1)
(-1.5, -3)

Answer 1

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.

1. **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 \(1\).

2. **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!