Question

(-3,4) , (0,3), (3,2), (6,1) Determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places as needed.

Answer 1

To determine the initial value (y-intercept) and the rate of change (slope) of the linear function represented by the points \((-3, 4)\), \((0, 3)\), \((3, 2)\), and \((6, 1)\), we can follow these steps:

1. **Identify the points**: From the given coordinates:
- Point A: \((-3, 4)\)
- Point B: \((0, 3)\)
- Point C: \((3, 2)\)
- Point D: \((6, 1)\)

2. **Determine the slope (rate of change)**: The slope (m) of a linear function passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can use two points; let's use \((0, 3)\) and \((6, 1)\):
\[
m = \frac{1 - 3}{6 - 0} = \frac{-2}{6} = -\frac{1}{3} \approx -0.333
\]

3. **Determine the initial value (y-intercept)**: Since the y-intercept is the y-value when \(x = 0\), we can directly see from the point \((0, 3)\) that the initial value (y-intercept) is:
\[
b = 3
\]

In conclusion, the initial value of the linear function is \(3\) and the rate of change (slope) is approximately \(-0.333\).

Thus, rounded to three decimal places, we have:
- Initial value: **3.000**
- Rate of change: **-0.333**