8.11: Drive Away
Drive Away – Interpret Graphs and Write Functions Rules
Teacher Notes
Each distancetime graph shows two lines representing the speeds of two drivers. Students first interpret the Fact to identify the driver of interest. Next they complete a TimeDistance table of values for the first 6 hours travelled. By inspecting the table of values and identifying relationships between entries in each line of the table, they write a rule that shows how the Distance \begin{align*}(D)\end{align*}
Solutions:
Drive Away 1
 15 mph

\begin{align*}D=15 \ t\end{align*}
D=15 t
Drive Away 2
 20 mph

\begin{align*}D=20 \ t\end{align*}
D=20 t
Drive Away – Interpret Graphs and Write Functions Rules
Fact: The graph shows the speeds of drivers, Axel and Bush, on city roads. Bush is traveling faster than Axel.
 What was Bush’s speed in miles per hour?
 Complete the table to show total number of miles traveled by Bush at that speed.
 Let \begin{align*}t\end{align*} represent number of hours and \begin{align*}D\end{align*} represent distance in number of miles. Write a rule to show how the number of miles \begin{align*}(D)\end{align*} is related to number of hours \begin{align*}(t)\end{align*}.
\begin{align*}D =\end{align*} ____________________
\begin{align*}& \mathbf{Describe:} && \text{The graph shows time in number of hours along the horizontal axis.}\\ &&& \text{Distance in number of miles is shown along the vertical axis. The two}\\ &&& \text{lines on the graph represent the speeds of Axel and Bush. The Fact}\\ &&& \text{indicates that Bush is traveling faster than Axel.}\\ \\ & \mathbf{My \ Job:} && \text{Use the Fact to figure out which line represents Bush. Complete the table}\\ &&& \text{for Bush. Write a rule to describe how the number of miles traveled is}\\ &&& \text{related to the number of hours of driving time.}\\ \\ & \mathbf{Plan:} && \text{Compare the lines with the Fact and decide which line represents Bush. }\\ &&& \text{Determine his average speed. Use that data to complete the table.}\\ &&& \text{Generalize from the data in the table. Construct the rule.}\\ \\ & \mathbf{Solve:} && \text{Bush is line S.}\\ &&& 1. \ \text{He was driving at a speed of} \ 30 \ \text{mph.}\\ &&& 2. \ \text{Complete the table using that speed to figure out the distances.}\end{align*}
\begin{align*}& 3. \ D=30 \ t\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\end{align*}
\begin{align*}& \mathbf{Check:} && \text{Use the rule to verify the data in the table.} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \\ &&& D=30 \times 1=30\\ &&& D=30 \times 2=60\\ &&& D=30 \times 3=90\\ &&& D=30 \times 4=120\\ &&& D=30 \times 5=150\\ &&& D=30 \times 6=180\end{align*}
Drive Away 1
Fact: The graph shows the speeds of drivers, Harold and French. Harold didn’t travel as fast as French.
 What was Harold’s speed in miles per hour?
 Complete the table to show total number of miles traveled by Harold at that speed.
 Let \begin{align*}t\end{align*} represent number of hours and \begin{align*}D\end{align*} represent distance in number of miles. Write a rule to show how the number of miles \begin{align*}(D)\end{align*} is related to number of hours \begin{align*}(t)\end{align*}.
\begin{align*}D =\end{align*} ____________________
Drive Away 2
Fact: The graph shows the speeds of drivers, Roberts and Clark. Roberts drove 10 mph slower than Clark.
 What was Clark’s speed in miles per hour?
 Complete the table to show total number of miles traveled by Clark at that speed.
 Let \begin{align*}t\end{align*} represent number of hours and \begin{align*}D\end{align*} represent distance in number of miles. Write a rule to show how the number of miles \begin{align*}(D)\end{align*} is related to number of hours \begin{align*}(t)\end{align*}.
\begin{align*}D =\end{align*} ____________________
Extra for Experts: Drive Away – Interpret Graphs and Write Functions Rules
Drive Away Extra 1
Fact: The graph shows the speeds of drivers, Marx and Stevens. Marx drove 5 mph faster than Stevens.
 What was Marx’s speed in miles per hour?
 Complete the table to show total number of miles traveled by Marx at that speed.
 Let \begin{align*}t\end{align*} represent number of hours and \begin{align*}D\end{align*} represent distance in number of miles. Write a rule to show how the number of miles \begin{align*}(D)\end{align*} is related to number of hours \begin{align*}(t)\end{align*}.
\begin{align*}D =\end{align*} ____________________
Drive Away Extra 2
Fact: The graph shows the speeds of drivers, Ellsworth and Stewart. The speed limit on Highway 999 is 55 mph. Ellsworth obeyed the speed limit. Stuart did not.
 What was Ellsworth’s speed in miles per hour?
 Complete the table to show total number of miles traveled by Ellsworth at that speed.
 Let \begin{align*}t\end{align*} represent number of hours and \begin{align*}D\end{align*} represent distance in number of miles. Write a rule to show how the number of miles \begin{align*}(D)\end{align*} is related to number of hours \begin{align*}(t)\end{align*}.
\begin{align*}D =\end{align*} ____________________
Solutions:
Drive Away Extra 1
 25 mph
 \begin{align*}D = 25 \ t\end{align*}
Drive Away Extra 2
 50 mph
 \begin{align*}D = 50 \ t\end{align*}
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