The relationship between the distance driven by the car and the time taken can be described using a linear relationship. Here's how to characterize this relationship:
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Linear Graph: If you were to plot the distance traveled (y-axis) against time (x-axis), the graph would be a straight line. The slope of this line represents the speed of the car, which in this case is 40 miles per hour.
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Starting Point: The line begins at the origin (0,0), indicating that at time zero, the distance traveled is also zero.
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Slope: For every hour that passes (1 hour, 2 hours, etc.), the car travels an additional 40 miles. Thus, the slope of the line is 40 miles/hour. This constant slope reflects the constant speed of the car.
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Distance Calculation: The distance traveled can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] In this case:
- After 1 hour: \(40 \text{ miles/hour} \times 1 \text{ hour} = 40 \text{ miles}\)
- After 2 hours: \(40 \text{ miles/hour} \times 2 \text{ hours} = 80 \text{ miles}\)
- After \(t\) hours: \(40t\) miles.
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Interpretation: This indicates a constant rate of increase in distance over time. The relationship is predictable; every hour results in a consistent increase in distance.
In summary, the relationship between time and distance for this car is linear, indicating that its speed is constant at 40 miles per hour, and it can be modeled by the equation \( \text{Distance} = 40 \times \text{Time} \).