Question

Use the image to answer the question. (2,0) (-3,2.5)(0,1)
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 ()

Answer 1

To determine the initial value and the rate of change of the linear function based on the points you've provided, we can use the coordinates of the points:

1. **Initial Value**: The initial value of a linear function (often referred to as the y-intercept) occurs when \( x = 0 \). From the points given, we see that at \( (0, 1) \), the value of the function is 1. Therefore, the initial value is **1**.

2. **Rate of Change**: The rate of change (or slope) of the linear function can be calculated using the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let's use two of the points, for example, \( (-3, 2.5) \) and \( (0, 1) \):
- \( y_2 = 1 \), \( y_1 = 2.5 \)
- \( x_2 = 0 \), \( x_1 = -3 \)

Plugging in these values gives us:
\[
\text{slope} = \frac{1 - 2.5}{0 - (-3)} = \frac{-1.5}{3} = -0.5
\]

Thus, the rate of change is **-0.5**.

To summarize:
- The initial value is **1**
- The rate of change is **-0.5**