Question

The linear function graphed below represents Tim's age in the years since he was married. Which of these statements is correct?

1) The initial value is 22, and the rate of change is 1.
2) The initial value is 22, and the rate of change is 15.
3) The initial value is 32, and the rate of change is 1.
4) The initial value is 32, and the rate of change is 15.

Answer 1

The correct statement is that the initial value is 22, and the rate of change is 15.

Step-by-step explanation:

The correct statement is:

1. The initial value is 22, and the rate of change is 15.

From the graph, we can see that the y-intercept (initial value) is 22 because the graph starts at the point (0, 22). The rate of change is the slope of the line, which represents how much the y-value (Tim's age) changes for each unit increase in the x-value (years since he was married). To determine the rate of change, we can choose any two points on the line and calculate the slope using the formula: rate of change = (change in y)/(change in x).

Let's choose two points: (0, 22) and (2, 52).

change in y = 52 - 22 = 30

change in x = 2 - 0 = 2

rate of change = 30/2 = 15

Therefore, the correct statement is that the initial value is 22, and the rate of change is 15.