8.14: Pedal Power
Pedal Power – Write Functions Rules from Graphs and Tables
Teacher Notes
Presented with line graphs representing two bikers’ speeds and a Fact about their relative speeds, students complete Distance-Time tables for each biker, and write functions to represent the relationship between number of miles and number of hours traveled for each biker. All line graphs show time in number of hours on the horizontal axis and distance in number of miles on the vertical axis.
Solutions
Time (Number of hours) | Spiro Distance (Number of miles) | Hendricks Distance (Number of miles) |
---|---|---|
0 | 0 | 0 |
1 | 0 | 6 |
2 | 3 | 12 |
3 | 6 | 18 |
4 | 9 | 24 |
5 | 12 | 30 |
Spiro: \begin{align*}D = 3(t-1)\end{align*}
Hendricks: \begin{align*}D = 6t\end{align*}
Time (Number of hours) | Kelly Distance (Number of miles) | Finley Distance (Number of miles) |
---|---|---|
0 | 0 | 0 |
1 | 0 | 6 |
2 | 0 | 12 |
3 | 8 | 18 |
4 | 16 | 24 |
5 | 24 | 30 |
Kelly: \begin{align*}D = 8(t-2)\end{align*}
Finley: \begin{align*}D = 6t\end{align*}
Solutions
Time (Number of hours) | Robinson Distance (Number of miles) | Cranston Distance (Number of miles) |
---|---|---|
0 | 0 | 0 |
1 | 0 | 10 |
2 | 5 | 20 |
3 | 10 | 30 |
4 | 15 | 40 |
5 | 20 | 50 |
Robinson: \begin{align*}D = 5(t-1)\end{align*}
Cranston: \begin{align*}D = 10t\end{align*}
Time (Number of hours) | Landis Distance (Number of miles) | Bricknell Distance (Number of miles) |
---|---|---|
0 | 0 | 0 |
1 | 0 | 4 |
2 | 0 | 8 |
3 | 0 | 12 |
4 | 8 | 16 |
5 | 16 | 20 |
Landis: \begin{align*}D = 8(t-3)\end{align*}
Bricknell: \begin{align*}D = 4t\end{align*}
Pedal Power – Write Functions Rules from Graphs and Tables
Fact: Judson left on the bike hike one hour after Connor and biked at a faster speed than Connor.
Use the Fact and the graph. Complete the table for each biker showing distance traveled. Write a function to show the relationship between number of miles traveled \begin{align*}(D)\end{align*}
\begin{align*}& \mathbf{Describe:} && \text{The graph is a Distance-Time graph and shows two lines. One line is} \\ & && \text{steeper than the other. One line starts where}\ t = 0.\ \text{The other line starts} \\ & && \text{where}\ t = 1.\ \text{The Fact identifies two bikers, Judson and Connors}. \\ & && \text{Judson left one hour after Connors and rode faster than Connors}. \\ \\ & \mathbf{My \ Job:} && \text{Use the graph and the Fact to figure out which line represents each biker}. \\ & && \text{Use the graph data to complete the table for each biker. Write the function} \\ & && \text{that shows the relationship between Distance and Time for each biker}. \\ \\ & \mathbf{Plan:} && \text{Use the Fact and graph to identify the line that represents Judson} \\ & && \text{Complete the table for Judson using points on the line. Write the} \\ & && \text{function rule. Do the same for Connors}. \\ \\ & \mathbf{Solve:} && \text{Since Judson leaves later than Connors,}\ \mathbf{line\ b}\ \text{represents Judson. Judson’s} \\ & && \text{number of hours is one less than the number of hours Connors bikes}. \\ & && \text{Judson’s line is steeper. This means that Judson is biking faster than Connors}.\end{align*}
Time (Number of hours) | Judson Distance (Number of miles) | Connors Distance (Number of miles) |
---|---|---|
0 | 0 | 0 |
1 | 0 | 5 |
2 | 10 | 10 |
3 | 20 | 15 |
4 | 30 | 20 |
5 | 40 | 25 |
\begin{align*}& && \text{Judson}:\ D = 10(t - 1) \\ & && \text{Connors}:\ D = 5t\end{align*}
\begin{align*}& \mathbf{Check:} && \text{Replace variables in the functions with their values. Check results}\\ & &&\text{with data in the table}.\end{align*}
Judson \begin{align*}D = 10(t - 1)\end{align*} | Connors \begin{align*}D = 5t\end{align*} | |
---|---|---|
For \begin{align*}t = 1\end{align*} | \begin{align*}0 = 10(1 - 1)\end{align*} | \begin{align*}5 = 5 \times 1\end{align*} |
For \begin{align*}t = 2\end{align*} | \begin{align*}10 = 10(2 - 1)\end{align*} | \begin{align*}10 = 5 \times 2\end{align*} |
For \begin{align*}t = 3\end{align*} | \begin{align*}20 = 10(3 - 1)\end{align*} | \begin{align*}15 = 5 \times 3\end{align*} |
For \begin{align*}t = 4\end{align*} | \begin{align*}30 = 10(4 - 1)\end{align*} | \begin{align*}20 = 5 \times 4\end{align*} |
For \begin{align*}t = 5\end{align*} | \begin{align*}40 = 10(5 - 1)\end{align*} | \begin{align*}25 = 5 \times 5\end{align*} |
Pedal Power 1 – Write Functions Rules from Graphs and Tables
Fact: Spiro left 1 hour after Hendricks and biked at a slower speed.
Use the Fact and the graph. Complete the table for each biker showing distance traveled. Write a function to show the relationship between number of miles traveled \begin{align*}(D)\end{align*} and number of hours \begin{align*}(t)\end{align*} traveled for each biker.
Pedal Power 2 – Write Functions Rules from Graphs and Tables
Fact: Kelly left 2 hours after Finley and biked at a faster speed.
Use the Fact and the graph. Complete the table for each biker showing distance traveled. Write a function to show the relationship between number of miles traveled \begin{align*}(D)\end{align*} and number of hours \begin{align*}(t)\end{align*} traveled for each biker.
Pedal Power 3 – Write Functions Rules from Graphs and Tables
Fact: Robinson left 1 hour after Cranston and biked at half of Cranston’s speed.
Use the Fact and the graph. Complete the table for each biker showing distance traveled. Write a function to show the relationship between number of miles traveled \begin{align*}(D)\end{align*} and number of hours \begin{align*}(t)\end{align*} traveled for each biker.
Pedal Power 4 – Write Functions Rules from Graphs and Tables
Fact: Landis left 3 hours after Bricknell and biked twice as fast as Bricknell.
Use the Fact and the graph. Complete the table for each biker showing distance traveled. Write a function to show the relationship between number of miles traveled \begin{align*}(D)\end{align*} and number of hours \begin{align*}(t)\end{align*} traveled for each biker.