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

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

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

Answer 1

To determine the initial value and the rate of change of the linear function from the graph described:

1. Initial Value: The initial value of a linear function (y-intercept) is the value of y when x = 0. According to the points given, one of the points is (0, 0), indicating that the initial value is 0.

2. Rate of Change: The rate of change (slope) can be determined by calculating the change in y over the change in x between two points on the line. Using the points (0.5, 1) and (0, 0):

   \[ \text{Rate of Change (slope)} = \frac{\Delta y}{\Delta x} = \frac{1 - 0}{0.5 - 0} = \frac{1}{0.5} = 2. \]

Based on these calculations, the initial value is 0, and the rate of change is 2.

Therefore, the correct response is:

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