Question

the graph shows the distance in miles of a runner over x hours. what is the average rate of speed over the interval 9, 11? (graph: title
unning\, x - axis labeled \time (in hours)\ with values 0, 2, 4, 6, 8, 10, 12, 14; y - axis labeled \distance (in miles)\ with values 0, 2, 4, 6, 8, 10, 12, 14, 16. points on the graph: (0,0), (5,1), (9,6), (11,11). options: 2, \\(\frac{2}{5}\\), \\(\frac{5}{2}\\), 1)

Explanation:

Step1: Recall average rate formula

The average rate of change (speed here) over \([a, b]\) is \(\frac{f(b) - f(a)}{b - a}\).

Step2: Identify \(a, b, f(a), f(b)\)

Here, \(a = 9\), \(b = 11\), \(f(9)=6\), \(f(11)=11\).

Step3: Calculate average rate

Substitute into formula: \(\frac{11 - 6}{11 - 9}=\frac{5}{2}\).

Answer:

\(\frac{5}{2}\) (corresponding to the option with \(\frac{5}{2}\))