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.

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

b. The initial value is 0, and the rate of change is 12.

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

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

1 answer

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

This can be determined by identifying any point on the line (here, point (0,0)) and calculating the slope from one of the other points. In this case, the slope is rise/run = (1 - 0) / (0.5 - 0) = 2. Therefore, the rate of change is 2.
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