Sketch a graph that could represent Diamond's family's distance from home vs. time.
Understand the Problem
The question is asking us to sketch a graph representing the distance of Diamond's family from their house over time, considering their movements described in the scenario.
Answer
The graph consists of an increase, a flat line, a decrease, and another increase representing Diamond's family's journey away from and back to their house over time.
Answer for screen readers
The graph will display a distance vs. time relationship with distinct slopes and horizontal line segments:
- Increase from (0, 0) to (t1, d1)
- A flat line from (t1, d1) to (t2, d1) (stop for gas)
- Decrease from (t2, d1) to (t3, 0) (return to home)
- Increase from (t3, 0) to (t4, d2) (drive away again)
Steps to Solve
- Identify the Phases of the Trip Break down the movement into specific phases based on the information provided:
- First, they drove away from their house.
- They stopped at a gas station, which indicates no change in distance for a period.
- After leaving the gas station, they returned to their house, reversing their distance.
- Finally, they drove away from their house again.
- Assign Distances and Time Intervals Create a timeline for the trip based on the information:
- Let the family's distance from home increase as they drive away (e.g., distance increases to 10 miles).
- When they stop to get gas, the distance remains constant.
- Driving back to the house will decrease the distance back to 0.
- Driving away from home again will increase the distance.
- Sketch the Graph Using the identified phases:
- Start from the origin (0 distance).
- Increase the distance to a certain point as they drive away.
- Draw a horizontal line representing the stop at the gas station.
- Afterward, draw a downward slope back to zero as they return home.
- Finally, create an upward slope again as they drive away.
- Label the Axes Make sure to label the horizontal axis as "Time" and the vertical axis as "Distance from Home."
The graph will display a distance vs. time relationship with distinct slopes and horizontal line segments:
- Increase from (0, 0) to (t1, d1)
- A flat line from (t1, d1) to (t2, d1) (stop for gas)
- Decrease from (t2, d1) to (t3, 0) (return to home)
- Increase from (t3, 0) to (t4, d2) (drive away again)
More Information
This graph illustrates the family's journey on vacation, highlighting key points where their distance from home changes. It effectively captures motion dynamics: away from home, stationary, returning home, and finally leaving again.
Tips
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