Question

show what you know
elizas family went on a long road trip.
this graph shows their distance over time.
determine the average rate of change for each interval.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). Here, \(x\) represents time (in hours) and \(y\) represents distance (in miles). For the interval \(4\) to \(6\) hours, \(x_1 = 4\), \(f(x_1)=175\), \(x_2 = 6\), and \(f(x_2)=275\).

Step2: Substitute the values into the formula

Substitute the values into the formula \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\). We get \(\frac{275 - 175}{6 - 4}\).

Step3: Simplify the expression

First, calculate the numerator: \(275-175 = 100\). Then, calculate the denominator: \(6 - 4=2\). So, \(\frac{100}{2}=50\).

Answer:

\(50\)