# 8.11: Drive Away

**At Grade**Created by: CK-12

**Drive Away – Interpret Graphs and Write Functions Rules**

**Teacher Notes**

Each distance-time 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 Time-Distance 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*}, or number of miles traveled, relates to the amount of time \begin{align*}(t)\end{align*}, or number of hours of travel.

**Solutions:**

**Drive Away 1**

- 15 mph
- \begin{align*}D=15 \ t\end{align*}

**Drive Away 2**

- 20 mph
- \begin{align*}D=20 \ t\end{align*}

**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.

\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.

\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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