Question

8.f.5
create a distance vs. time graph showing adam’s distance from his house. label each segment of the graph.
a. adam left his friend brody’s house and started walking home.
b. adam realized he left his phone at brody’s so he turned around to get it.
c. adam left brody’s a second time and started to walk home.
d. adam stopped halfway to talk to a friend he passed.
e. adam then quickly ran home to make it in time for dinner.
image of a boy walking and a distance-time graph axis

Explanation:

Step1: Analyze Segment A

Adam starts at Brody’s (distance from his house is constant, say \(d\)) and walks home, so distance from his house decreases linearly over time. So the graph is a line with negative slope from \((t_0, d)\) to some \((t_1, d_1)\) where \(d_1

Step2: Analyze Segment B

He turns around to go back to Brody’s, so distance from his house increases linearly (positive slope) back to \(d\) at time \(t_2\).

Step3: Analyze Segment C

Leaves Brody’s again, distance from his house decreases linearly (negative slope) until halfway (let's say distance \(d_3=\frac{d}{2}\)) at time \(t_3\).

Step4: Analyze Segment D

Stops to talk, so distance from his house is constant (horizontal line) from \(t_3\) to \(t_4\).

Step5: Analyze Segment E

Runs home, so distance from his house decreases linearly (steeper negative slope than segment A/C) from \(d_3\) to \(0\) at time \(t_5\).

To draw:

• Vertical axis: Distance from Adam’s house (labeled).
• Horizontal axis: Time (labeled).
• Plot points:
• Start at (0, \(d\)) (Brody’s house distance from Adam’s).
• Segment A: Line down to ( \(t_1\), \(d_1\) ).
• Segment B: Line up back to ( \(t_2\), \(d\) ).
• Segment C: Line down to ( \(t_3\), \(d/2\) ).
• Segment D: Horizontal line to ( \(t_4\), \(d/2\) ).
• Segment E: Steeper line down to ( \(t_5\), 0 ).

Label each segment with A, B, C, D, E.

Answer:

The graph should have 5 segments:

• A: Decreasing line (walking home first time).
• B: Increasing line (returning to Brody’s).
• C: Decreasing line (walking home second time, halfway).
• D: Horizontal line (stopped to talk).
• E: Steeper decreasing line (running home).

Label axes "Time" (x) and "Distance from Adam’s House" (y), and each segment with A, B, C, D, E.