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 −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.
Based on the given graph, it is clear that the line intersects the y-axis at a point with a y-coordinate of 2. This means that the initial value is 2.
Regarding the rate of change, it can be determined by examining the slope of the line. The slope is the amount the line increases or decreases vertically (the y-coordinate) for every increase of one unit horizontally (the x-coordinate).
From the graph, it can be seen that for every increase of one unit in the x-coordinate, the line increases by 2 units in the y-coordinate. Therefore, the rate of change is 2.
Therefore, the correct answer is: The initial value is 2, and the rate of change is 2.