Use the linear model to make a prediction the line of best fit y equals 0.37x + 5 represents the tools you pay after driving a specific number of miles what prediction can be made based on this line of best fit
If you drop 10 mi you would pay $42 you can spend less than $30 to go 75 miles you can spend $42 to drive a hundred miles you can drive 50 miles and spend less than $20
If you drop 10 mi you would pay $42 you can spend less than $30 to go 75 miles you can spend $42 to drive a hundred miles you can drive 50 miles and spend less than $20
Answers
Answered by
GPT-4o mini
To use the line of best fit, given by the equation \( y = 0.37x + 5 \), we need to identify what \( x \) and \( y \) represent. Here, \( x \) is the number of miles driven, and \( y \) represents the toll paid.
1. **For the statement, "If you drive 10 miles, you would pay $42":**
Plugging in \( x = 10 \) into the equation:
\[
y = 0.37(10) + 5 = 3.7 + 5 = 8.7
\]
This means if you drive 10 miles, you would pay $8.70, not $42. Therefore, the statement is incorrect according to the model.
2. **For the statement, "You can spend less than $30 to go 75 miles":**
Plugging in \( x = 75 \) into the equation:
\[
y = 0.37(75) + 5 = 27.75 + 5 = 32.75
\]
This means to drive 75 miles, you would pay approximately $32.75, which is more than $30. Hence, this statement is also incorrect according to the model.
3. **For the statement, "You can spend $42 to drive 100 miles":**
Plugging in \( x = 100 \) into the equation:
\[
y = 0.37(100) + 5 = 37 + 5 = 42
\]
This statement is correct, according to the model.
4. **For the statement, "You can drive 50 miles and spend less than $20":**
Plugging in \( x = 50 \) into the equation:
\[
y = 0.37(50) + 5 = 18.5 + 5 = 23.5
\]
This means to drive 50 miles, you would pay approximately $23.50, which is greater than $20. Hence, this statement is also incorrect according to the model.
### Summary of Findings:
- The only prediction that aligns with the line of best fit is that you can spend $42 to drive 100 miles.
- The other statements regarding 10 miles, 75 miles, and 50 miles do not hold true according to the linear model provided.
1. **For the statement, "If you drive 10 miles, you would pay $42":**
Plugging in \( x = 10 \) into the equation:
\[
y = 0.37(10) + 5 = 3.7 + 5 = 8.7
\]
This means if you drive 10 miles, you would pay $8.70, not $42. Therefore, the statement is incorrect according to the model.
2. **For the statement, "You can spend less than $30 to go 75 miles":**
Plugging in \( x = 75 \) into the equation:
\[
y = 0.37(75) + 5 = 27.75 + 5 = 32.75
\]
This means to drive 75 miles, you would pay approximately $32.75, which is more than $30. Hence, this statement is also incorrect according to the model.
3. **For the statement, "You can spend $42 to drive 100 miles":**
Plugging in \( x = 100 \) into the equation:
\[
y = 0.37(100) + 5 = 37 + 5 = 42
\]
This statement is correct, according to the model.
4. **For the statement, "You can drive 50 miles and spend less than $20":**
Plugging in \( x = 50 \) into the equation:
\[
y = 0.37(50) + 5 = 18.5 + 5 = 23.5
\]
This means to drive 50 miles, you would pay approximately $23.50, which is greater than $20. Hence, this statement is also incorrect according to the model.
### Summary of Findings:
- The only prediction that aligns with the line of best fit is that you can spend $42 to drive 100 miles.
- The other statements regarding 10 miles, 75 miles, and 50 miles do not hold true according to the linear model provided.