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.
what is the rate of change of the function?
rate of change = \frac{change in y - values}{change in x - values}=\frac{22 - 10}{2 - 0}=6
what does the rate of change tell you?
eliana bikes 6 miles? home every hour.

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function is given by $\frac{\text{change in }y\text{-values}}{\text{change in }x\text{-values}}$.

Step2: Identify values from the table

We have two points $(x_1,y_1)=(0,10)$ and $(x_2,y_2)=(2,22)$. The change in $y$ is $y_2 - y_1=22 - 10 = 12$, and the change in $x$ is $x_2 - x_1=2 - 0 = 2$.

Step3: Calculate the rate of change

$\text{Rate of change}=\frac{22 - 10}{2 - 0}=\frac{12}{2}=6$.

Step4: Interpret the rate of change

Since the distance $y$ (distance from home) is increasing as time $x$ increases, a positive rate of change means Eliana bikes 6 miles farther from home every hour.

Answer:

6; farther from