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Let's break down the problem and analyze each answer choice to determine which two statements are **TRUE** regarding the comparison of the two pricing equations.

### Problem Summary
1. **Last year's rate:** The golf driving range charged **$19.98 per hour** with no flat fee.
   - Equation: $ y = 19.98x $, where $ x $ is the number of hours, and $ y $ is the total cost.
2. **This year's rate:** The range charges the same hourly rate (**$19.98 per hour**) but adds a **flat fee of $4.99**.
   - Equation: $ y = 19.98x + 4.99 $.

### Analyzing the Choices
Let's go through each option in detail:

- **Option A:** "The graphs have the same y-intercepts. Both graphs start at the origin because there is no initial charge for each year."
  - This is **FALSE**. This year's equation has a flat fee of $4.99, meaning it does not start at the origin. Only last year's equation starts at the origin.

- **Option B:** "The graphs have different slopes. The graph for this year's price has a slope that is 4.99 more than last year's price."
  - This is **FALSE**. The slope (rate per hour) is the same for both years: $19.98. The difference is in the y-intercept, not the slope.

- **Option C:** "The graphs have the same slopes. The graph for each year's price has a slope of 24.97."
  - This is **FALSE**. The slope is $19.98 for both years, not $24.97.

- **Option D:** "The graphs have the same slopes. The graph for each year's price has a slope of 19.98."
  - This is **TRUE**. Both equations share the same hourly rate, so the slopes are identical at $19.98.

- **Option E:** "The graphs have different y-intercepts. The graph for this year’s price is shifted up 4.99 units from last year’s price."
  - This is **TRUE**. This year’s equation has a y-intercept of $4.99, while last year’s y-intercept was $0, reflecting the flat fee difference.

- **Option F:** "The graphs have different y-intercepts. The graph for this year’s price is shifted up 19.98 units from last year’s price."
  - This is **FALSE**. The y-intercept difference is $4.99, not $19.98.

### Conclusion
The two true statements are:
- **D:** The graphs have the same slopes. The graph for each year's price has a slope of 19.98.
- **E:** The graphs have different y-intercepts. The graph for this year’s price is shifted up 4.99 units from last year’s price.

### Final Answer
The correct choices are **D and E**.

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Would you like a further explanation of any part of this solution? Here are some related questions that might deepen your understanding:

1. How does the flat fee affect the y-intercept of the graph?
2. Why is the slope the same for both years, even with the new flat fee?
3. What would the graph look like if the hourly rate had changed instead?
4. How would you interpret the slope and y-intercept in a real-world context?
5. How can you determine shifts in a graph by comparing y-intercepts?

**Tip:** Remember, the slope represents the rate of change, while the y-intercept represents any initial charge or starting value in real-world scenarios.

Last year, a golf driving range charged $19.98 per hour to hit golf balls. This year, the golf driving range charges the same hourly rate, but there is a flat fee of $4.99. Which TWO statements are TRUE when comparing the graphs of the equations?

Analyze and compare the graphs of two linear equations representing golf driving range prices from last year and this year. Learn how the introduction of a flat fee affects the y-intercept while the slope remains unchanged. Suitable for students in Grades 8-10.

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