Question

Determine the initial value and the rate of change of the linear function given in the graph. (1 point) The initial value is , and the rate of change is

If is the points graphed are 0, 0 and 2, 3

The line is increasing

Answer 1

To find the initial value and the rate of change of the linear function represented by the points (0, 0) and (2, 3), we can follow these steps:

1. **Initial Value**: The initial value of a linear function is the y-value when x = 0. From the point (0, 0), we see that the initial value is:
\[
\text{Initial value} = 0
\]

2. **Rate of Change (slope)**: The rate of change (slope) can be calculated using the formula:
\[
\text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points (0, 0) and (2, 3):
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (2, 3) \)

Plugging in these values:
\[
\text{slope} = \frac{3 - 0}{2 - 0} = \frac{3}{2}
\]

Thus, the initial value is \(0\) and the rate of change is \(\frac{3}{2}\).

In summary:
- Initial value: **0**
- Rate of change: **\(\frac{3}{2}\)**