Slope and y-intercepts Quick Check

Question

5 of 55 of 5 Items

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

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 −6
, and the rate of change is 2.

Answer 1

To determine the initial value and rate of change of the linear function from the given information, we need to analyze the points provided:

1. The points given are:

   • (−1.5, −3)
   • (0, 0)
   • (0.5, 1)

2. The initial value corresponds to the y-intercept of the line. From the point (0, 0), we can see that when x = 0, y = 0. Hence, the initial value (y-intercept) is 0.

3. To find the rate of change (slope), we can calculate it using two points on the line. Let's use the points (0, 0) and (0.5, 1):

   • The slope (m) is calculated as: \[ m = \frac{\text{change in y}}{\text{change in x}} = \frac{1 - 0}{0.5 - 0} = \frac{1}{0.5} = 2 \]

Thus, the rate of change is 2.

Putting it all together, the initial value is 0 and the rate of change is 2.

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