To determine the initial value and rate of change based on the points provided, we can interpret these points as pairs (x, y), where \(y\) is the dependent variable and \(x\) is the independent variable.
You provided the following points:
- \((2, 0)\)
- \((0, 1)\)
- \((-3, 2.5)\)
To find the initial value and rate of change, we will consider a linear relationship between \(x\) and \(y\). The equation of a line can be expressed as:
\[ y = mx + b \]
where \(m\) is the slope (rate of change) and \(b\) is the y-intercept (initial value).
Finding the Slope (Rate of Change)
We can calculate the slope using any two points. Let's use \((0, 1)\) and \((2, 0)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 1}{2 - 0} = \frac{-1}{2} = -0.5 \]
This means the rate of change \(m\) is \(-0.5\).
Finding the Initial Value (Y-Intercept)
Using the point \((0, 1)\), we can see that when \(x = 0\), \(y = 1\). Hence, the initial value \(b\) (y-intercept) is \(1\).
Summary
- Initial Value (Y-Intercept): \(b = 1\)
- Rate of Change (Slope): \(m = -0.5\)
If you have specific requirements for the data points, please let me know!