the graph shows the distances traveled by two runners over several minutes. which runner is moving at a…
the graph shows the distances traveled by two runners over several minutes. which runner is moving at a slower rate? select from the drop - down menu to correctly complete the statement. runner is moving at a slower rate.
Answer
Explanation:
Step1: Understand the relationship between rate and the graph
The rate of a runner (speed) in a distance - time graph is given by the slope of the line. The formula for slope (m=\frac{y_2 - y_1}{x_2 - x_1}). A smaller slope means a slower rate.
Step2: Compare the slopes of the two lines
For a non - vertical line passing through the origin ((0,0)) and another point ((x,y)), the slope (m = \frac{y}{x}). Let's assume we pick a common (x) - value (say (x = 4) units on the time axis). For Runner A, if we assume at (x = 4), (y) (distance) for Runner A is larger than (y) for Runner B. Using the slope formula (m=\frac{y}{x}) (since (x_1 = 0,y_1 = 0)), if (x) is the same ((x>0)) and (y_A>y_B), then (m_A=\frac{y_A}{x}>m_B=\frac{y_B}{x}).
Another way: The steeper the line in a distance - time graph (where (y) is distance and (x) is time), the higher the speed. Since Runner B's line is less steep than Runner A's line.
Answer:
B. Runner B