To determine the initial value and the rate of change of the linear function from the given points, we can first identify the points and use them to find the equation of the line.
We have the points:
- (-3, 4)
- (0, 3)
- (3, 2)
- (6, 1)
Step 1: Find the Rate of Change (Slope)
The rate of change (slope \( m \)) of a linear function can be calculated using any two points on the line. The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's use the points (0, 3) and (3, 2):
- \((x_1, y_1) = (0, 3)\)
- \((x_2, y_2) = (3, 2)\)
Calculating the slope:
\[ m = \frac{2 - 3}{3 - 0} = \frac{-1}{3} \]
Step 2: Determine the Initial Value (y-intercept)
The initial value (y-intercept) is the value of \(y\) when \(x = 0\). From the given points, when \(x = 0\), \(y = 3\).
Final Result
Thus, the initial value and the rate of change are:
- The initial value is \(3.000\)
- The rate of change is \(-0.333\) (after rounding to three decimal places)
So, the answer is:
- The initial value is 3.000, and the rate of change is -0.333.