5. 
Carson practices each day to prepare for an upcoming race. He starts the day by running 2
 miles and then walking at a rate of 4
 miles per hour.

Which representations show the relationship between the total number of miles he covers in a day, y
, and the number of hours he walks, x
?

Select THREE correct answers.
A.y=2x+4

B.
Number of Hours
Walked	Total Number of
Miles
1
6
112
8
2
10

C.
D.​​​​​​​y=4x+2

E.
Number of Hours
Walked	Total Number of
Miles
1
6
112
7
2
8

F.

Let's analyze the problem carefully to determine which of the given representations are correct.

Carson starts by running 2 miles each day, then walks at a rate of 4 miles per hour. We want to find the total number of miles \( y \) he covers in a day, based on the number of hours \( x \) he spends walking.

The equation for this situation can be written as:
\[
y = 2 + 4x
\]
where:
- \( 2 \) represents the miles he runs at the beginning of the day, and
- \( 4x \) represents the miles he covers walking at a rate of 4 miles per hour for \( x \) hours.

Now, let's evaluate the options:

1. **Option A: \( y = 2x + 4 \)**  
   This equation is incorrect because it suggests that the rate of walking is 2 miles per hour, and the constant distance covered is 4 miles. This does not match the situation described.

2. **Option B: Number of Hours Walked - Total Number of Miles Table (1, 6; 2, 10)**  
   If \( x = 1 \), then \( y = 2 + 4(1) = 6 \).  
   If \( x = 2 \), then \( y = 2 + 4(2) = 10 \).  
   This matches the table, so **this is a correct representation**.

3. **Option C: (No clear content, but if it matches \( y = 2 + 4x \), it could be correct.)**  
   We need more information to assess Option C.

4. **Option D: \( y = 4x + 2 \)**  
   This equation correctly represents the situation: 4 miles per hour walking rate multiplied by the number of hours \( x \), plus 2 miles that he starts with. **This is correct.**

5. **Option E: Number of Hours Walked - Total Number of Miles Table (1, 6; 2, 8)**  
   If \( x = 1 \), then \( y = 6 \), which is correct. But if \( x = 2 \), then \( y = 10 \), not 8. Therefore, **this is incorrect.**

6. **Option F: (No content provided here, so cannot be evaluated.)**

### Correct Answers
Based on the analysis:
- **B (Correct table)**
- **D (Correct equation)**
- **If more information aligns with \( y = 4x + 2 \), possibly C or F could be correct.**

Would you like further details or have any questions?

---

### Related Questions:
1. What would the equation be if Carson runs 3 miles instead of 2?
2. How would the graph of \( y = 4x + 2 \) look like on a coordinate plane?
3. How can we determine if a table correctly represents a linear equation?
4. What happens to the total distance \( y \) if Carson increases his walking speed?
5. How would the equation change if Carson also bikes at a different rate?

### Tip:
Always substitute values back into an equation to verify if a given representation (table or equation) matches the described situation.

Carson practices each day to prepare for an upcoming race. He starts the day by running 2 miles and then walking at a rate of 4 miles per hour. Which representations show the relationship between the total number of miles he covers in a day, y, and the number of hours he walks, x? Select THREE correct answers: A) y=2x+4, B) Number of Hours Walked - Total Number of Miles (1,6; 2,10), C), D) y=4x+2, E) Number of Hours Walked - Total Number of Miles (1,6; 2,8), F).

Explore how to find the total miles Carson covers in a day using a linear equation y = 2 + 4x. This math problem involves representing word problems with equations, creating tables, and analyzing linear relationships. Suitable for students in Grades 6-8.

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