Determine the initial value and the rate of change of the linear function as given in the graph. (1 point)
The initial value is −6, 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.
The initial value is 0, and the rate of change is 1/2.
The correct answer is:
The initial value is 0, and the rate of change is 2.
correct?
Apologies for the error. The correct answer is:
The initial value is −6, and the rate of change is 2.
To determine the initial value and rate of change of a linear function from a graph, we need to identify two key points on the graph.
In this case, we can see that the graph crosses the y-axis at -6, which means the initial value is -6. This eliminates options 2, 3, and 4.
Next, we need to find the rate of change, which is the slope of the line. We can do this by finding the difference in the y-coordinates (vertical change) and dividing it by the difference in the x-coordinates (horizontal change) of two points on the line.
Let's take two points on the line, such as (0,-6) and (1,-4). The vertical change is 2 (from -6 to -4), and the horizontal change is 1 (from 0 to 1).
So, the rate of change (slope) is 2/1 = 2.
Therefore, the correct answer is "The initial value is -6, and the rate of change is 2."