Question

Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows on both ends passes through the following closed points: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 3 right parenthesis.

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
.
Remaining Attempts : 3
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page 26 of 27

Answer 1

To determine the initial value and the rate of change of the linear function given in the graph, we can analyze the points provided.

1. **Identify the initial value**: The initial value of a linear function is the y-intercept, which is the value of y when x = 0. From the points given, the function passes through (0, 0). Therefore, the initial value is:

**Initial value = 0**

2. **Calculate the rate of change**: The rate of change (slope) of a linear function can be calculated using the formula:

\[
\text{Slope (m)} = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (0, 0) and (2, 3):

\[
m = \frac{3 - 0}{2 - 0} = \frac{3}{2}
\]

Thus, the rate of change is:

**Rate of change = \(\frac{3}{2}\)**

In summary:
- The initial value is **0**, and the rate of change is **\(\frac{3}{2}\)**.