Question

eliana rides her bike from her home to the park, where she meets a friend. they bike together to a nearby town. the table shows elianas distance from home, y, as a function of the time she bikes with her friend, x. how can you find the rate of change? rate of change = ? / change in x - values change in y - values time (h), x distance from home (mi), y 0 10 2 22 4 34

Explanation:

Step1: Identify change in y - values

The change in \(y\)-values is found by subtracting the initial \(y\)-value from the final \(y\)-value. For the given data, when \(x\) changes from \(0\) to \(2\), \(y\) changes from \(10\) to \(22\). So, change in \(y = 22 - 10=12\). When \(x\) changes from \(2\) to \(4\), \(y\) changes from \(22\) to \(34\), and change in \(y=34 - 22 = 12\) as well. In general, we can take two - point values. Let's take the first and the second row: \(\Delta y=22 - 10\).

Step2: Identify change in x - values

The change in \(x\)-values is found by subtracting the initial \(x\)-value from the final \(x\)-value. When \(y\) changes from \(10\) to \(22\), \(x\) changes from \(0\) to \(2\). So, \(\Delta x=2 - 0=2\).

Step3: Calculate rate of change

The rate of change is given by the formula \(\text{rate of change}=\frac{\text{change in }y\text{-values}}{\text{change in }x\text{-values}}\). Substituting \(\Delta y = 12\) and \(\Delta x=2\) into the formula, we get \(\text{rate of change}=\frac{22 - 10}{2 - 0}=\frac{12}{2}=6\).

Answer:

\(6\)