Your teacher surveyed the class to determine the number of hours that each student spent on social media. Your teacher created a table and scatterplot graph that displayed 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 y -intercept. What is the average grade if a student was on social media for 10 hours?
Your teacher surveyed the class to determine the number of hours that each student spent on social media. Your teacher created a table and scatterplot graph that displayed the number of hours, x , and the average final grade percentage, y , based on the hours. Using the equation of the trend line of the data, y=–7.2x+98.9 , predict the average final grade percentage, to the nearest whole number, if a student spent 10 hours on social media.(1 point)
Responses
The average final grade is 92% if a student spent 10 hours on social media.
The average final grade is 92% if a student spent 10 hours on social media.
The average final grade is 27% if a student spent 10 hours on social media.
The average final grade is 27% if a student spent 10 hours on social media.
The average final grade is 99% if a student spent 10 hours on social media.
The average final grade is 99% if a student spent 10 hours on social media.
The average final grade is 7.2 if a student spent 10 hours on social media.
The y-intercept of the trend line equation is 98.9. In this context, the y-intercept represents the average final grade when a student spends zero hours on social media.
If a student was on social media for 10 hours, we can substitute x=10 into the equation to find the predicted average final grade:
y = -7.2x + 98.9
y = -7.2(10) + 98.9
y = -72 + 98.9
y = 26.9
Therefore, if a student was on social media for 10 hours, the average predicted final grade would be 26.9.
The correct statement is:
The average final grade is 27% if a student spent 10 hours on social media.
To interpret the y-intercept in the context of this problem, you need to understand what it signifies. In the equation y = -7.2x + 98.9, the y-intercept refers to the value of y when x is equal to zero.
In this case, x represents the number of hours spent on social media, and y represents the average final grade. So, when x is zero, it means a student did not spend any time on social media.
Interpreting the y-intercept, we can conclude that if a student did not spend any time on social media (x = 0), their average final grade would be 98.9.
To find the average grade if a student was on social media for 10 hours, you can substitute x = 10 into the equation and solve for y:
y = -7.2x + 98.9
y = -7.2(10) + 98.9
y = -72 + 98.9
y = 26.9
Therefore, if a student were on social media for 10 hours, their average final grade would be approximately 26.9.