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

Question

UpStudy AI · Accepted Answer

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.
For every 10 additional miles driven, the family can expect to see one more out-of-state plate.

Real Tutor Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Statistics Questions