https://file.aiquickdraw.com/mathbot/file/1725854891395lax5bsg2.jpg

The image contains a table showing city and highway miles per gallon (MPG) for four cars, and two parts of a problem. Let me break it down and guide you through:

### Table:
| Model | City MPG | Highway MPG |
|-------|----------|-------------|
| Car A | 33       | 47          |
| Car B | 42       | 46          |
| Car C | 31       | 40          |
| Car D | 30       | 38          |

### Question Part (a):
You are asked to find the **best equation** that relates highway MPG to city MPG for these cars.

### Question Part (b):
Next, you are supposed to use the equation from part (a) to predict the highway MPG for a car that gets 48 MPG in the city.

### Additional information:
There's a suggested form for the equation:  
\[ y = mx + b \]  
where \(x\) is the city MPG, \(y\) is the highway MPG, and \(m\) and \(b\) are constants to be determined.

### Step-by-step approach:
1. We need to find the equation of the best-fit line using the data from the table. This can be done by finding the slope \(m\) and intercept \(b\) of the line.
2. Use this equation to predict the highway MPG for the given city MPG (48).

Let me calculate the equation of the line first using the data.The equation of the best-fit line relating highway MPG (\(y\)) to city MPG (\(x\)) is:

\[
y = 0.544x + 24.24
\]

### Part (b):
To predict the highway MPG for a car with 48 city MPG, we'll substitute \(x = 48\) into the equation.

Let me calculate that next.Using the equation \( y = 0.544x + 24.24 \), the predicted highway MPG for a car with 48 city MPG is approximately **50.37 MPG**.

### Summary:
- The best-fit equation is: \( y = 0.544x + 24.24 \).
- For a car with 48 city MPG, the predicted highway MPG is about 50.37 MPG.

Would you like more details or have any further questions?

### Related questions:
1. How do we calculate the slope \(m\) of a line from data points?
2. What does the \(r\)-value in linear regression represent?
3. How would this equation change with more data points?
4. How do we interpret the intercept in this equation?
5. How does linear regression handle outliers in data?

**Tip:** In linear regression, the \(r^2\) value (coefficient of determination) helps measure how well the equation fits the data!

You are asked to find the best equation that relates highway MPG to city MPG for four cars and use it to predict the highway MPG for a car that gets 48 MPG in the city.

Explore how to predict highway MPG from city MPG using a linear regression model. This detailed guide includes the formula y = mx + b, where m and b are constants derived from car MPG data, suitable for college-level students.

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