Question

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Slope and y-intercepts Practice
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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
.

Answer 1

To determine the initial value (y-intercept) and the rate of change (slope) of the linear function represented by the line in the given graph, we can analyze the information provided.

1. **Initial Value (y-intercept)**:
The initial value of the function is the y-coordinate where the line intersects the y-axis. From the given points, the line passes through the point (0, 0). Therefore, the initial value is:
- **Initial Value**: 0

2. **Rate of Change (Slope)**:
The slope (rate of change) of a linear function can be calculated using the formula:
\[
\text{Slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
In this case, we can use the points (0, 0) and (2, 3):
- \(y_1 = 0\), \(y_2 = 3\)
- \(x_1 = 0\), \(x_2 = 2\)

Substituting these values into the slope formula:
\[
\text{Slope} = \frac{3 - 0}{2 - 0} = \frac{3}{2} = 1.5
\]

Thus,
- The initial value is **0**,
- The rate of change is **1.5**.

So the final answer is:
- Initial value: **0**
- Rate of change: **1.5**