Question
Owen is going to drive from his house to City A without stopping. Let DD represent Owen's distance from City A tt hours after leaving his house. A graph of DD is shown below. Write an equation for DD then state the slope of the graph and determine its interpretation in the context of the problem.
0
Number of Hours Driving
Distance Remaining to City A (Miles)
t
D
0
Number of Hours Driving
Distance Remaining to City A (Miles)
Answer
Attempt 1 out of 2
D, equalsD=
The slope of the function is
which reveals
0
Number of Hours Driving
Distance Remaining to City A (Miles)
t
D
0
Number of Hours Driving
Distance Remaining to City A (Miles)
Answer
Attempt 1 out of 2
D, equalsD=
The slope of the function is
which reveals
Answers
GPT-4o mini
To write an equation for \( D(t) \), which represents the distance Owen has left to travel to City A at time \( t \), we need to analyze the graph and find the relationship between time and distance.
Let's assume you have a linear graph. When \( t \) is 0, let’s say the distance \( D \) to City A starts at \( D_0 \) miles. If we establish that Owen is driving at a constant speed, the distance remaining decreases as time increases.
The general form of a linear equation can be expressed as:
\[
D(t) = D_0 - mt
\]
where:
- \( D_0 \) is the starting distance from City A,
- \( m \) is the rate at which distance decreases over time, and
- \( t \) is the time in hours driving.
### Finding the Slope and its Interpretation
1. **Slope:**
The slope \( m \) is the rate of change of distance with respect to time, which represents how much distance decreases per hour. For example, if the slope is -60, it means that for each hour Owen drives, he reduces the distance to City A by 60 miles.
2. **Interpretation:**
This negative slope indicates that the distance Owen has left to travel decreases as he spends more time driving. In the context of this problem, it shows Owen's speed; if the slope \( m \) is 60 miles per hour, it implies that Owen is driving towards City A at a speed of 60 miles per hour.
### Conclusion
If you'd like me to create a specific equation or fill in particular values, please provide the specifics from the graph, such as \( D_0 \) or the total distance, as well as the observed slope.
Let's assume you have a linear graph. When \( t \) is 0, let’s say the distance \( D \) to City A starts at \( D_0 \) miles. If we establish that Owen is driving at a constant speed, the distance remaining decreases as time increases.
The general form of a linear equation can be expressed as:
\[
D(t) = D_0 - mt
\]
where:
- \( D_0 \) is the starting distance from City A,
- \( m \) is the rate at which distance decreases over time, and
- \( t \) is the time in hours driving.
### Finding the Slope and its Interpretation
1. **Slope:**
The slope \( m \) is the rate of change of distance with respect to time, which represents how much distance decreases per hour. For example, if the slope is -60, it means that for each hour Owen drives, he reduces the distance to City A by 60 miles.
2. **Interpretation:**
This negative slope indicates that the distance Owen has left to travel decreases as he spends more time driving. In the context of this problem, it shows Owen's speed; if the slope \( m \) is 60 miles per hour, it implies that Owen is driving towards City A at a speed of 60 miles per hour.
### Conclusion
If you'd like me to create a specific equation or fill in particular values, please provide the specifics from the graph, such as \( D_0 \) or the total distance, as well as the observed slope.