Question

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

A graph titled Tim's Age During Marriage has years of marriage on the x-axis and Tim's Age on the y-axis. Points are at (22, 54), (37, 69), (52, 84).
The initial value is 22, and the rate of change is 1.
The initial value is 22, and the rate of change is 15.
The initial value is 32, and the rate of change is 1.
The initial value is 32, and the rate of change is 15.

Answer 1

Slope = (69−54)/(37−22) = 15/15 = 1, so rate of change = 1.
Using y = x + b with (22,54): 54 = 22 + b → b = 32.

So the correct statement: the initial value is 32, and the rate of change is 1.