The table represents a bicycle rental cost in dollars as a function of time in hours. Bicycle Rental \begin{tabular}{|c|c|} \hline $\begin{array}{c}\text { Time } \\ \text { (hours) }\end{array}$ & $\begin{array}{c}\text { Cost } \\ \text { (\$) }\end{array}$ \\ \hline 0 & 0 \\ \hline 2 & 10 \\ \hline 4 & 20 \\ \hline 6 & 30 \\ \hline 8 & 40 \\ \hline \end{tabular} Which explains whether or not the function represents a direct variation? This function represents a direct variation because it passes through the origin and has a constant rate of change of $\$ 5$ per hour. This function represents a direct variation because it has a positive, constant rate of change of $\$ 10$ per hour. This function does not represent a direct variation because it does not represent the cost for 1 hour. This function does not represent a direct variation because the function rule for the cost is to add $\$ 10$, not multiply by a constant. Mark this and return Save and Exit Next Submit
Solution
Step 1 ：The question is asking whether the function represents a direct variation or not. A function represents a direct variation if it passes through the origin and has a constant rate of change.
Step 2 ：From the table, we can see that the function does pass through the origin (0,0) and the rate of change (slope) is constant.
Step 3 ：The slope can be calculated by taking the difference in y-values divided by the difference in x-values. In this case, the slope is \((10-0)/(2-0) = 5\).
Step 4 ：Therefore, the function represents a direct variation with a constant rate of change of $5 per hour.
Step 5 ：Final Answer: This function represents a direct variation because it passes through the origin and has a constant rate of change of \(\boxed{5}\) per hour.
