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To solve this problem, we need to interpret the graph provided and then find an equation for \( D \), which represents Owen's distance from City A as a function of the number of hours \( t \) he has been driving.

### Step 1: Understanding the Graph
The graph shows a linear relationship between the number of hours driving (\( t \)) and the distance from City A (\( D \)).

### Step 2: Identifying Key Points
Let's identify the key points from the graph:
- The starting point (when \( t = 0 \)): \( D \) is at 250 miles.
- The ending point (when \( t = 5 \)): \( D \) is at 0 miles.

### Step 3: Determining the Slope
The slope of the line (\( m \)) can be calculated using the formula:
\[
m = \frac{\Delta D}{\Delta t} = \frac{D_2 - D_1}{t_2 - t_1}
\]
From the graph, the change in distance (\( \Delta D \)) is from 250 miles to 0 miles, and the change in time (\( \Delta t \)) is from 0 hours to 5 hours.
\[
m = \frac{0 - 250}{5 - 0} = \frac{-250}{5} = -50 \text{ miles per hour}
\]

### Step 4: Writing the Equation
The equation of a line in slope-intercept form is \( D = mt + b \), where \( b \) is the y-intercept. From the graph, the y-intercept (\( b \)) is 250 miles (the distance at \( t = 0 \)).
\[
D = -50t + 250
\]

### Step 5: Interpretation of the Slope
The slope of -50 means that for each hour Owen drives, his distance from City A decreases by 50 miles.

### Final Equation and Interpretation
\[
\boxed{D = -50t + 250}
\]
This equation represents Owen's distance from City A after \( t \) hours of driving. The slope of -50 indicates that Owen is driving towards City A at a constant speed of 50 miles per hour.

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Would you like more details or have any questions on this? Here are some related questions you might find helpful:

1. What is the significance of the y-intercept in this context?
2. How would the graph change if Owen drove faster or slower?
3. What would the equation look like if City A was further away?
4. How can we interpret the slope if it were positive?
5. What other types of problems can be modeled with linear equations like this?
6. How does the concept of slope apply to real-world driving scenarios?
7. Can you determine the total distance Owen will have traveled after a certain number of hours?
8. How would the equation change if Owen started his journey at a different time?

**Tip:** Understanding the slope as a rate of change can help you interpret many real-life scenarios modeled by linear equations.

Understand how to interpret Owen's distance from City A using linear equations. Learn step-by-step how to derive the equation D = -50t + 250 from a given graph, identifying key points and understanding the slope as a rate of change. Suitable for Grades 7-9 students studying linear equations and graph interpretation.

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