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 at both ends passes through the following closed points: left parenthesis negative 1.5 comma negative 3 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 0.5 comma 1 right parenthesis.

Determine the initial value and the rate of change of the linear function as given in the graph.

(1 point)
Responses

The initial value is −6
, and the rate of change is 2.
The initial value is negative 6 , and the rate of change is 2.

The initial value is 0, and the rate of change is 2.
The initial value is 0, and the rate of change is 2.

The initial value is 0, and the rate of change is 12
.
The initial value is 0, and the rate of change is Start Fraction 1 over 2 End Fraction .

The initial value is 2, and the rate of change is 2.
The initial value is 2, and the rate of change is 2.
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Answer 1

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

The line passes through the points:

1. (-1.5, -3)

2. (0, 0)

3. (0.5, 1)

4. Rate of Change (Slope): To find the slope of the line (rate of change), we can choose any two points on the line. Using the points (0, 0) and (0.5, 1):

   \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{0.5 - 0} = \frac{1}{0.5} = 2 \]

   So, the rate of change is 2.

5. Initial Value (y-intercept): The initial value refers to 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 y-intercept is 0.

Given this information, we can conclude that:

• The initial value is 0.
• The rate of change is 2.

Thus, the correct response is:

The initial value is 0, and the rate of change is 2.