Question

this table shows the distance traveled by a car and the cars average speed on different days. given that the days are the independent variable, which dependent variable has a constant rate of change? what is the constant rate of change? day average speed (mph) distance (miles) 3 55 495 4 58 660 5 63 825 6 65 990 7 68 1,155

Explanation:

Step1: Calculate rate of change for distance

To find the rate of change of a variable with respect to days, we use the formula $\text{Rate of change}=\frac{\Delta y}{\Delta x}$, where $y$ is the variable and $x$ is the number of days. For distance, $\Delta x = 1$ (as the days increase by 1 each time).
For the first - two data points (day 3 and day 4):
$\Delta\text{Distance}=660 - 495=165$, $\Delta\text{Day}=4 - 3 = 1$, rate of change $=\frac{660 - 495}{4 - 3}=165$.
For day 4 and day 5: $\Delta\text{Distance}=825 - 660 = 165$, $\Delta\text{Day}=5 - 4=1$, rate of change $=\frac{825 - 660}{5 - 4}=165$.
For day 5 and day 6: $\Delta\text{Distance}=990 - 825 = 165$, $\Delta\text{Day}=6 - 5 = 1$, rate of change $=\frac{990 - 825}{6 - 5}=165$.
For day 6 and day 7: $\Delta\text{Distance}=1155 - 990 = 165$, $\Delta\text{Day}=7 - 6 = 1$, rate of change $=\frac{1155 - 990}{7 - 6}=165$.

Step2: Calculate rate of change for speed

For the first - two data points (day 3 and day 4): $\Delta\text{Speed}=58 - 55 = 3$, $\Delta\text{Day}=4 - 3=1$, rate of change $=\frac{58 - 55}{4 - 3}=3$.
For day 4 and day 5: $\Delta\text{Speed}=63 - 58 = 5$, $\Delta\text{Day}=5 - 4 = 1$, rate of change $=\frac{63 - 58}{5 - 4}=5$. Since the rate of change of speed is not constant.

Answer:

The dependent variable with a constant rate of change is Distance. The constant rate of change is 165 miles per day.