Question

examine the distance-time graph.
distance ( km )
time ( h )
text alternative
a. which line represents travel at the fastest speed? justify your answer.
keyboard help

Explanation:

Step1: Recall speed formula

Speed is calculated as \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \). For a distance - time graph, the slope of the line \( m=\frac{\Delta y}{\Delta x}=\frac{\text{Distance}}{\text{Time}} \), so the slope of the line in a distance - time graph represents speed.

Step2: Analyze slope of lines

In a distance - time graph, a steeper line has a greater slope. Line A is steeper than lines B and C. Since slope represents speed (\( \text{Speed}=\frac{\text{Distance}}{\text{Time}} \)), a greater slope means a greater speed. So, for the same amount of time, the line with the steeper slope (line A) will cover more distance, indicating a faster speed.

Answer:

Line A represents travel at the fastest speed. Because in a distance - time graph, the slope of the line is equal to speed (\( \text{Speed}=\frac{\text{Distance}}{\text{Time}} \)), and line A has the steepest slope among lines A, B, and C, meaning it has the greatest speed.