Question
Maddie's math teacher plots student grades on weekly quizzes against the number of hours they work on classwork a week and then draws the line of best fit.
line starts at 1,55 (4,75)(5,85)(6,95)(7,90)(8,100) line ends
Write an equation in slope-intercept form of the trend line.
(1 point)
Responses
y=x+55
y is equal to x plus 55
y=5x+55
y is equal to 5 x plus 55
y=−5x
y is equal to negative 5 x
y=x+60
y is equal to x plus 60
Question 2
Part B
According to the data, what is the best prediction for a student's quiz grade if they spend 5 hours working on their math classwork a week?
(1 point)
Responses
90
90
75
75
71
71
81
81
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line starts at 1,55 (4,75)(5,85)(6,95)(7,90)(8,100) line ends
Write an equation in slope-intercept form of the trend line.
(1 point)
Responses
y=x+55
y is equal to x plus 55
y=5x+55
y is equal to 5 x plus 55
y=−5x
y is equal to negative 5 x
y=x+60
y is equal to x plus 60
Question 2
Part B
According to the data, what is the best prediction for a student's quiz grade if they spend 5 hours working on their math classwork a week?
(1 point)
Responses
90
90
75
75
71
71
81
81
Skip to navigation
Answers
Answered by
GPT-4o mini
To find the equation of the line of best fit in slope-intercept form (y = mx + b), we can first calculate the slope (m) using two points from the data.
Given the points:
- (1, 55)
- (4, 75)
- (5, 85)
- (6, 95)
- (7, 90)
- (8, 100)
We can use the points (1, 55) and (8, 100) for our slope calculation:
1. Find the slope (m):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{100 - 55}{8 - 1} = \frac{45}{7} \approx 6.43
\]
2. Using the slope and one of the points to find the y-intercept (b). We can use the point (1, 55):
\[
y = mx + b \\
55 = (6.43)(1) + b \\
b = 55 - 6.43 \\
b \approx 48.57
\]
So, the equation of the line (rounded for simplicity) would be:
\[
y \approx 6.43x + 48.57
\]
However, it looks like the options provided imply a simpler version, so let's verify each:
1. **y = x + 55** (Not close)
2. **y = 5x + 55** (Not close)
3. **y = -5x** (Not relevant)
4. **y = x + 60** (Not close)
Given these options and if we assume the teacher used a simpler approximation, based on your data of (1, 55) to (8, 100), "y = 5x + 55" seems to be the closest approximation for an average slope calculation.
**For Part B**:
Now, to predict the quiz grade for a student who works 5 hours a week, we can substitute \( x = 5 \) into the best-fit equation derived from our calculations. Using a simple slope for chart approximation—if we take the option:
\[
y = 5(5) + 55 = 25 + 55 = 80
\]
Given the possible answer choices, the best prediction from options is:
- **81**
Thus, the final answers are:
- **Part A:** y = 5x + 55 (as the closest approximation)
- **Part B:** 81
Given the points:
- (1, 55)
- (4, 75)
- (5, 85)
- (6, 95)
- (7, 90)
- (8, 100)
We can use the points (1, 55) and (8, 100) for our slope calculation:
1. Find the slope (m):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{100 - 55}{8 - 1} = \frac{45}{7} \approx 6.43
\]
2. Using the slope and one of the points to find the y-intercept (b). We can use the point (1, 55):
\[
y = mx + b \\
55 = (6.43)(1) + b \\
b = 55 - 6.43 \\
b \approx 48.57
\]
So, the equation of the line (rounded for simplicity) would be:
\[
y \approx 6.43x + 48.57
\]
However, it looks like the options provided imply a simpler version, so let's verify each:
1. **y = x + 55** (Not close)
2. **y = 5x + 55** (Not close)
3. **y = -5x** (Not relevant)
4. **y = x + 60** (Not close)
Given these options and if we assume the teacher used a simpler approximation, based on your data of (1, 55) to (8, 100), "y = 5x + 55" seems to be the closest approximation for an average slope calculation.
**For Part B**:
Now, to predict the quiz grade for a student who works 5 hours a week, we can substitute \( x = 5 \) into the best-fit equation derived from our calculations. Using a simple slope for chart approximation—if we take the option:
\[
y = 5(5) + 55 = 25 + 55 = 80
\]
Given the possible answer choices, the best prediction from options is:
- **81**
Thus, the final answers are:
- **Part A:** y = 5x + 55 (as the closest approximation)
- **Part B:** 81