Question
A study was done to investigate the use of text messaging over time. The correlating linear model is shown, where x represents the number of years after 2006, and y represents the average number of text messages a person sends monthly. Interpret the y-intercept.
A.
In 2005, a person sent an average of 65 text messages per month.
B.
In 2005, a person sent an average of 146 text messages per month.
C.
In 2006, a person sent an average of 146 text messages per month.
D.
In 2006, a person sent an average of 65 text messages per month.
A.
In 2005, a person sent an average of 65 text messages per month.
B.
In 2005, a person sent an average of 146 text messages per month.
C.
In 2006, a person sent an average of 146 text messages per month.
D.
In 2006, a person sent an average of 65 text messages per month.
Answers
GPT-4o mini
To interpret the y-intercept of the correlating linear model, we need to understand what the y-intercept represents in the context of this situation. In the equation of a linear model where \( y \) represents the average number of text messages per month and \( x \) represents the number of years after 2006, the y-intercept occurs when \( x = 0 \).
When \( x = 0 \), it corresponds to the year 2006 (since \( x \) is the number of years after 2006). Therefore, the y-intercept indicates the average number of text messages a person sent in 2006.
To choose the correct interpretation from the options given:
- Option A states the average for 2005, which is not correct for the y-intercept.
- Option B also states the average for 2005, which is not correct for the y-intercept.
- Option C correctly identifies the average for 2006.
- Option D misidentifies the year, as it states 2006 but gives the wrong average.
Thus, the correct interpretation of the y-intercept is:
**C. In 2006, a person sent an average of 146 text messages per month.**
When \( x = 0 \), it corresponds to the year 2006 (since \( x \) is the number of years after 2006). Therefore, the y-intercept indicates the average number of text messages a person sent in 2006.
To choose the correct interpretation from the options given:
- Option A states the average for 2005, which is not correct for the y-intercept.
- Option B also states the average for 2005, which is not correct for the y-intercept.
- Option C correctly identifies the average for 2006.
- Option D misidentifies the year, as it states 2006 but gives the wrong average.
Thus, the correct interpretation of the y-intercept is:
**C. In 2006, a person sent an average of 146 text messages per month.**