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.
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.
Answers
GPT-4o mini
To understand Tim's age as a function of the years since he was married, we can analyze the points provided and the general characteristics of linear functions.
1. The points provided are:
- (22, 54) indicating that after 22 years of marriage, Tim is 54 years old.
- (37, 69) indicating that after 37 years of marriage, Tim is 69 years old.
- (52, 84) indicating that after 52 years of marriage, Tim is 84 years old.
2. From the points, we can determine the initial value, which corresponds to how old Tim was when he got married (time = 0). We will use the first point (22, 54) to find the initial age before he was married:
- Since 22 years after marriage he is 54 years old, we can calculate Tim's age when married:
\[
\text{Age when married} = 54 - 22 = 32
\]
3. Next, we calculate the rate of change, which represents how much older Tim gets each year. Observing the age increase:
- In 15 years (from 22 to 37), Tim's age increases from 54 to 69 (an increase of 15 years). This shows that Tim's age increases by 1 year for each year of marriage.
Putting it all together:
- The initial age (when married) is 32.
- The rate of change (increase in age per year) is 1.
Thus, the correct statement among the provided options is:
**The initial value is 32, and the rate of change is 1.**
1. The points provided are:
- (22, 54) indicating that after 22 years of marriage, Tim is 54 years old.
- (37, 69) indicating that after 37 years of marriage, Tim is 69 years old.
- (52, 84) indicating that after 52 years of marriage, Tim is 84 years old.
2. From the points, we can determine the initial value, which corresponds to how old Tim was when he got married (time = 0). We will use the first point (22, 54) to find the initial age before he was married:
- Since 22 years after marriage he is 54 years old, we can calculate Tim's age when married:
\[
\text{Age when married} = 54 - 22 = 32
\]
3. Next, we calculate the rate of change, which represents how much older Tim gets each year. Observing the age increase:
- In 15 years (from 22 to 37), Tim's age increases from 54 to 69 (an increase of 15 years). This shows that Tim's age increases by 1 year for each year of marriage.
Putting it all together:
- The initial age (when married) is 32.
- The rate of change (increase in age per year) is 1.
Thus, the correct statement among the provided options is:
**The initial value is 32, and the rate of change is 1.**