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 change in the x - values from 0 to 2? rate of change = \frac{change in y - values}{change in x - values}=\frac{22 - 10}{?} time (h), x distance from home (mi), y 0 10 2 22 4 34

Explanation:

Step1: Identify the x - values

The initial x - value is \(x_1 = 0\) and the final x - value is \(x_2=2\).

Step2: Calculate the change in x - values

The change in x - values \(\Delta x=x_2 - x_1\). Substitute \(x_1 = 0\) and \(x_2 = 2\) into the formula, so \(\Delta x=2-0 = 2\).
For the rate - of - change formula, the denominator (change in x - values) from \(x = 0\) to \(x = 2\) is 2.

Answer:

The change in the \(x\) - values from 0 to 2 is 2. The denominator in the rate - of - change formula for the given time interval is 2.