Use the image to answer the question.

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 \(\frac{3}{2}\).