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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
.
Remaining Attempts : 3
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Answer 1

To determine the initial value and the rate of change of the linear function represented by the line on the coordinate plane, we start with the two key points on the line: (0, 0) and (2, 3).

1. Initial value: The initial value occurs where the line intersects the y-axis. From the point (0, 0), we can see that when x = 0, y = 0. Thus, the initial value is:

   Initial value = 0

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

Therefore, putting it all together:

• The initial value is 0,
• The rate of change is 1.5 (or \( \frac{3}{2} \)).

Final answer: The initial value is 0, and the rate of change is 1.5.