The equation for the line of best fit is \( y=\frac{1}{10} x+4 \). In this context, what is the meaning of the slope? By driving 4 additional miles, the family could expect to see one additional out-of-state plate. By driving 10 additional miles, the family could expect to see one additional out-of-state plate. On a given trip, the family could expect to see at least 4 out-of-state plates. On a given trip, the family could expect to see plates from at least \( \frac{1}{10} \) of the states. Ther

In the equation for the line of best fit: \[ y = \frac{1}{10}x + 4 \] **Here:** - \( y \) represents the expected number of out-of-state plates. - \( x \) represents the number of miles driven. **Understanding the Slope (\( \frac{1}{10} \)):** - The slope indicates how much \( y \) changes for each additional unit of \( x \). - Specifically, a slope of \( \frac{1}{10} \) means that for **every 10 additional miles driven**, the family can expect to see **1 additional out-of-state plate**. **Why Option B is Correct:** - **Option B:** *By driving 10 additional miles, the family could expect to see one additional out-of-state plate.* This accurately interprets the slope: \[ \frac{1}{10} \text{ plate/mile} \times 10 \text{ miles} = 1 \text{ additional plate} \] **Why Other Options Are Incorrect:** - **Option A:** *By driving 4 additional miles, the family could expect to see one additional out-of-state plate.* - Calculation: \[ \frac{1}{10} \times 4 = 0.4 \text{ plates} \] So, 4 miles would result in less than half an additional plate, not a full one. - **Option C:** *On a given trip, the family could expect to see at least 4 out-of-state plates.* - The number 4 is the **y-intercept**, representing the expected number of plates when no miles are driven. It doesn't relate to the slope. - **Option D:** *On a given trip, the family could expect to see plates from at least \( \frac{1}{10} \) of the states.* - This misinterprets the slope as a fraction of states rather than the number of additional plates per mile driven. **Conclusion:** The slope of \( \frac{1}{10} \) in the equation \( y = \frac{1}{10}x + 4 \) means that **for every 10 additional miles driven, the family can expect to see one additional out-of-state plate**. **Answer:** By driving 10 additional miles, the family could expect to see one additional out-of-state plate.