Drawing Distance-Time Graphs from Journey Stories

Algebra and Function Practice

A distance-time graph turns a journey story into a picture. The horizontal axis shows time and the vertical axis shows distance from the starting point. A flat segment means the traveller is stopped. A rising segment means moving away. A falling segment means returning. In this lesson you will build graphs from descriptions, mark stop segments, and compare slopes to show different speeds. All measurements use consistent units, and any numerical values chosen for practice are hypothetical examples.

Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.

Setting up axes and scale

Choose a time axis and a distance axis that fit the whole journey. Label each axis with its unit, such as minutes and kilometres. Pick a scale so the largest time and largest distance both fit on the grid. For example, if a journey lasts 60 minutes and reaches 12 km, a grid with 10 minutes per square and 2 km per square works. These numbers are hypothetical examples; always measure or read the actual values given in the journey description.

Plot the starting point at time zero and distance zero unless the story says otherwise. Then work through the journey in order, plotting each change of state: moving, stopped, or returning. Connect the points with straight segments. A stop is a horizontal segment because time passes but distance does not change.

1. Read the journey and list each time and distance pair in order.
2. Choose scales for time and distance that fit the largest values.
3. Plot the start at (0, 0) and each later point.
4. Connect points with straight segments and label stops as flat segments.

Marking stops and returns

A stop appears as a horizontal segment. If the traveller waits from 20 to 30 minutes at 5 km, plot (20, 5) and (30, 5) and join them with a flat line. A return appears as a falling segment. If the traveller goes back to the start, the distance decreases to zero. If the return is faster than the outward trip, the falling segment is steeper than the rising segment.

Label each stop segment clearly, for example with the word stop or a short note. Label the final position so the reader can see where the journey ends. Keep the graph neat so slopes are easy to compare.

1. Mark the beginning and end of every stop with points at the same distance.
2. Draw a horizontal segment between those points.
3. For a return, plot the lower distance at the later time.
4. Check that the final point matches the story's ending distance.

Using slopes to show speed

On a distance-time graph, a steeper segment means a faster speed. A gentle segment means a slower speed. A flat segment means zero speed. You do not need to calculate exact speeds to draw the graph, but comparing slopes helps you check that the picture matches the story. If the story says the return trip was quicker, the falling segment should be steeper than the rising segment.

When two segments have the same slope, the traveller moved at the same speed. When a segment is steeper, the distance changed more in the same amount of time. Use this check after drawing to catch mistakes such as a stop drawn as a slope or a fast return drawn too gently.

1. Compare each rising or falling segment with the others.
2. Make faster parts steeper and slower parts gentler.
3. Keep stops flat and clearly labelled.
4. Re-read the story and confirm each segment matches one part of the journey.

Checking your finished graph

After drawing, trace the graph from left to right and tell the journey aloud. Each segment should match one sentence or event in the description. Check that time always moves forward, that stops are flat, and that returns go downward. Confirm the final distance matches the story. If a point is misplaced, adjust it and redraw the segment.

A useful check is to list the plotted points and compare them with the journey description. Another check is to confirm that no segment goes backward in time. These simple checks catch most drawing errors before you submit your work.

1. Trace the graph and describe each segment in words.
2. Check that every stop is horizontal.
3. Check that every return segment falls.
4. Confirm the final point matches the ending distance.

Worked example

A cyclist starts at home. She rides for 20 minutes and reaches 4 km. She stops for 10 minutes. Then she rides back home, taking 15 minutes. Draw the distance-time graph and mark the stop.

Four practice exercises

Common mistakes

• Drawing a stop as a rising segment. A stop keeps distance the same while time passes, so draw a horizontal segment between two points at the same distance.
• Making a fast return less steep than a slow outward trip. A faster change in distance over the same time is steeper. Check the slopes against the story's speed clues.
• Plotting time backward or connecting points out of order. Work through the journey in time order and keep the time axis increasing from left to right.
• Forgetting to label axes or units. Write the unit on each axis, such as minutes and kilometres, so the graph can be read correctly.

Self-check rubric

• Axes are labelled with time and distance units.
• The starting point is plotted correctly, usually at (0, 0).
• Each journey event is represented by a correct segment in time order.
• Stops are drawn as horizontal segments and labelled.
• Returns are drawn as falling segments with appropriate steepness.
• The final point matches the ending distance in the story.
• The graph is neat enough to compare slopes and read points.

Questions and answers