Question
Your teacher surveyed the class to determine the number of hours that each student spent on social media. A table and scatterplot graph were created to display the number of hours and the average final grade based on the hours. The trend line (equation) for the data is y=−7.2x+98.9.
Interpret the slope. How many points does the average final grade decrease for 1 hour on social media?
a. the average final grade is 7.2 if a student spent 10 hours on social media
b. the average final grade is 27% if a student pent 10 hours on social media.
c. the average final grade is 92% if a student spent spent 10 hours on social media.
d. the average final grade is 99% if a student spent 10 hours on social media.
Interpret the slope. How many points does the average final grade decrease for 1 hour on social media?
a. the average final grade is 7.2 if a student spent 10 hours on social media
b. the average final grade is 27% if a student pent 10 hours on social media.
c. the average final grade is 92% if a student spent spent 10 hours on social media.
d. the average final grade is 99% if a student spent 10 hours on social media.
Answers
Answered by
GPT-4o mini
To interpret the slope of the trend line given by the equation \( y = -7.2x + 98.9 \):
In this equation, \( y \) represents the average final grade, and \( x \) represents the number of hours spent on social media. The slope of the line, which is -7.2, indicates that for each additional hour spent on social media, the average final grade decreases by 7.2 points.
Now, looking at the options provided:
- a. "the average final grade is 7.2 if a student spent 10 hours on social media" - This option does not accurately reflect the context and content of the trend line.
- b. "the average final grade is 27% if a student spent 10 hours on social media." - If a student spends 10 hours on social media, we calculate the final grade using the equation:
\( y = -7.2(10) + 98.9 = -72 + 98.9 = 26.9 \%). This has not been rounded but does not seem to provide a relevant average final grade in percentage terms.
- c. "the average final grade is 92% if a student spent 10 hours on social media." - The calculated final grade using the equation as previously shows that it won’t yield ”92%.”
- d. "the average final grade is 99% if a student spent 10 hours on social media." - Again, using the equation shows this isn't correct.
To summarize:
- The slope indicates the average final grade decreases by 7.2 points for each hour spent on social media. None of the options correctly compute a value from the equation when substituted with \( x = 10 \).
In this equation, \( y \) represents the average final grade, and \( x \) represents the number of hours spent on social media. The slope of the line, which is -7.2, indicates that for each additional hour spent on social media, the average final grade decreases by 7.2 points.
Now, looking at the options provided:
- a. "the average final grade is 7.2 if a student spent 10 hours on social media" - This option does not accurately reflect the context and content of the trend line.
- b. "the average final grade is 27% if a student spent 10 hours on social media." - If a student spends 10 hours on social media, we calculate the final grade using the equation:
\( y = -7.2(10) + 98.9 = -72 + 98.9 = 26.9 \%). This has not been rounded but does not seem to provide a relevant average final grade in percentage terms.
- c. "the average final grade is 92% if a student spent 10 hours on social media." - The calculated final grade using the equation as previously shows that it won’t yield ”92%.”
- d. "the average final grade is 99% if a student spent 10 hours on social media." - Again, using the equation shows this isn't correct.
To summarize:
- The slope indicates the average final grade decreases by 7.2 points for each hour spent on social media. None of the options correctly compute a value from the equation when substituted with \( x = 10 \).