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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
.

Answer 1

To determine the initial value and the rate of change of the linear function represented by the line passing through the points (0, 0) and (2, 3), we can proceed as follows:

1. Initial Value: This represents the y-intercept of the line, which is the value of y when x = 0. From the point (0, 0), we can see that the initial value is: \[ \text{Initial Value} = 0 \]

2. Rate of Change: This represents the slope (m) of the line, which can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] For the points (0, 0) and (2, 3):

   • \( (x_1, y_1) = (0, 0) \)
   • \( (x_2, y_2) = (2, 3) \)

   Plugging in the values: \[ m = \frac{3 - 0}{2 - 0} = \frac{3}{2} \]

Now, we can summarize our findings:

• The initial value is \( 0 \).
• The rate of change is \( \frac{3}{2} \).

Thus, the answers are:

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