Based on the line of best fit, the relationship between quiz score and time spent studying appears to be linear. To determine how much time someone should study to expect a quiz score of 94, we need to find the x-value where the corresponding y-value is 94.
From the given data points, we can see that as quiz scores increase from 58 to 82, the time spent on homework per week increases from 0 to 4 hours.
To find the equation of the line of best fit, we can calculate the slope using the formula:
slope = (change in y) / (change in x) = (82 - 58) / (4 - 0) = 24 / 4 = 6
Using the points (0, 58) and the slope of 6, we can write the equation of the line in the form y = mx + b:
y = 6x + b
Substitute the coordinates of the point (0, 58) into the equation to solve for the y-intercept (b):
58 = 6(0) + b
b = 58
Therefore, the equation of the line of best fit is y = 6x + 58.
To find out how much time someone should study to expect a quiz score of 94, we can substitute y = 94 into the equation and solve for x:
94 = 6x + 58
36 = 6x
x = 6
Therefore, someone should study 6 hours per week to expect a quiz score of 94.
William's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. Based on the line of best fit, how much time should someone study to expect a quiz score of 94?
0
x
y
0
(0,58)
(2,70)
(4,82)
Quiz Score
Time Spent on Homework per Week (hours)
Answer
Attempt 1 out of 3
3 answers
wrong
I apologize for the mistake in my previous response. Let's correct it:
From the given data points, we have the following:
(0, 58)
(2, 70)
(4, 82)
The line of best fit for these points can be determined by calculating the slope and y-intercept. The slope can be calculated using the formula:
m = (change in y) / (change in x)
m = (82 - 58) / (4 - 0) = 24 / 4 = 6
Now we can use the slope and one of the points (0, 58) to find the y-intercept (b) using the equation y = mx + b:
58 = 6(0) + b
b = 58
So, the equation of the line of best fit is:
y = 6x + 58
To find how much time should someone study to expect a quiz score of 94 (let y = 94), we substitute y = 94 into the equation:
94 = 6x + 58
6x = 36
x = 6
Therefore, someone should study 6 hours per week to expect a quiz score of 94.
From the given data points, we have the following:
(0, 58)
(2, 70)
(4, 82)
The line of best fit for these points can be determined by calculating the slope and y-intercept. The slope can be calculated using the formula:
m = (change in y) / (change in x)
m = (82 - 58) / (4 - 0) = 24 / 4 = 6
Now we can use the slope and one of the points (0, 58) to find the y-intercept (b) using the equation y = mx + b:
58 = 6(0) + b
b = 58
So, the equation of the line of best fit is:
y = 6x + 58
To find how much time should someone study to expect a quiz score of 94 (let y = 94), we substitute y = 94 into the equation:
94 = 6x + 58
6x = 36
x = 6
Therefore, someone should study 6 hours per week to expect a quiz score of 94.