Practice Maths

Time Graphs

Reading Time Graphs

Key Terms

time graph
a line graph where the horizontal axis (x-axis) represents time and the vertical axis shows a quantity that changes over time, such as distance, temperature, or volume
slope
the steepness of a line on a graph; a steeper slope means a faster rate of change
rate of change
how quickly a quantity increases or decreases over time; shown visually by how steep the line is
horizontal section
a flat (zero-slope) portion of a time graph, indicating no change in the quantity during that time interval

A time graph tells a story. The horizontal axis (x-axis) always represents Time. The vertical axis (y-axis) represents a changing quantity — like distance from home, temperature, or water level.

What the slope tells you:

  • Steep line going up — fast increase (e.g. running quickly away, temperature rising rapidly)
  • Gentle line going up — slow increase (e.g. walking slowly)
  • Flat (horizontal) line — no change (e.g. stationary, temperature holding steady)
  • Line going down — decreasing (e.g. returning home, temperature falling)
Hot Tip: Storytelling
Time graphs and stories go both ways. Given a graph, you can write the story. Given a story, you can sketch the graph.
Example: "Steep up, flat, gentle down" → "ran to the park, rested, then walked slowly home."

Worked Example

A person walks away from home at constant speed, waits, then returns home. Describe the distance-time graph.

Step 1 — The first section is a rising line. Distance from home is increasing, so the person is moving away.

Step 2 — The middle section is a flat (horizontal) line. Distance is not changing, so the person is stationary (waiting).

Step 3 — The final section is a falling line. Distance from home is decreasing, so the person is returning home. A steeper slope in this section means they are moving faster.

What Is a Time Graph?

A time graph is a line graph where the x-axis always represents time. The y-axis shows something that changes over time — distance, temperature, water level, or speed. Reading a time graph is like reading a story: the line tells you what happened and when.

Imagine you walk to the park, sit for a rest, then walk home. A distance-time graph of that trip would show the line going up (walking away), flat (resting), then back down (walking home).

What the Shape of the Line Tells You

The steepness (slope) of the line is the key to reading any time graph:

  • Steep line going up: fast increase — for example, running away from home quickly.
  • Gentle line going up: slow increase — walking slowly.
  • Flat (horizontal) line: no change at all. In a distance-time graph, flat means you are not moving. (Many students confuse "flat" with "moving at a steady speed" — that is wrong! Steady speed is still a diagonal line.)
  • Line going down: decreasing — returning closer to the starting point, or a temperature dropping.

A steeper line always means a faster rate of change. If two sections of a graph are both rising, the steeper one represents the faster speed.

Reading Values from a Time Graph

To read a specific value from a time graph:

  1. Find the time value you want on the x-axis.
  2. Go straight up to where the line is.
  3. Read across to the y-axis to get the value.

You can also work in reverse — to find when a particular value was reached, find it on the y-axis, go across to the line, then read down to the time axis. Always check the scale on both axes carefully before reading.

Sketching a Graph from a Description

Sometimes you are given a story and asked to sketch the graph. Work through the story stage by stage:

  • Identify each stage — e.g. "walks for 5 minutes, then stops for 2 minutes, then runs for 3 minutes."
  • Decide the direction for each stage: up, flat, or down.
  • Decide the steepness: a run should be steeper than a walk.
  • Mark approximate time lengths on the x-axis for each stage.
  • Connect the sections with straight lines (for constant speed).

Sketches do not need exact numbers — they just need to show the correct shape and direction for each stage of the story.

Critical distinction: A flat line means the quantity is not changing at all. In a distance-time graph, flat = stopped. A person moving at a steady (constant) speed produces a diagonal straight line, not a flat one. This is the most common misconception in this topic.

Creating a Graph from Data

When you have real data collected over time, turn it into a graph with these steps:

  1. Set up axes: time on the horizontal axis (label with units), the measured quantity on the vertical axis (label with units).
  2. Plot the data points from your table.
  3. Connect the dots with a line to reveal the pattern. Use a straight line between points for constant change; a curve for non-constant change.

Once the graph is drawn, use it to make predictions — read off values between your data points, or extend the line to estimate future values.

Practice Questions

  1. Boiling the Kettle Fluency

    The graph below shows the temperature of water in a kettle over time.

    Time Temp
    1. What is happening to the water temperature in the first (steep) section?
    2. Why does the line go flat at the top?

  2. Flat Lines Fluency

    In a Distance vs Time graph, what does a horizontal (flat) line represent?

  3. Comparing Speed Fluency

    Line A is steeper than Line B on a distance-time graph. Which object is moving faster — the one represented by Line A or Line B?

  4. Ben’s Commute Fluency

    The graph below shows Ben’s distance from home over time. Ben walked to the park, sat on a bench, then ran home.

    Time (mins) Dist (m)
    1. Which section of the graph represents Ben sitting on the bench? (First, Middle, or Last?)
    2. Did Ben take longer to walk to the park or to run home?

  5. Speed Calculation Understanding

    Using the graph in Question 4, assume Ben’s park is 400 m from his home.

    1. If it took him 10 minutes to walk to the park, what was his walking speed in metres per minute?
    2. If he ran home in 5 minutes, what was his running speed in metres per minute?

  6. The Bathtub Understanding

    A bath is filled with water, then someone sits in it for a while, and finally the plug is pulled and it drains.

    1. Filling: Does the water level line go up or down?
    2. Draining: Does the water level line go up or down?
    3. Sitting in it: Is the water level line flat, going up, or going down?

  7. Filling Jugs Understanding

    You fill two containers with water at a constant flow rate. Jug A has straight vertical sides (like a cylinder). Jug B is wide at the bottom and narrow at the top.

    1. Which jug will produce a straight-line graph for water level vs time? Which will produce a curved line?
    2. Here is the data for Jug A:
      Time (sec)02468
      Level (cm)0481216
      Does the water level rise by the same amount every 2 seconds?
    3. Is the relationship for Jug A linear or non-linear? How can you tell from the table?

  8. Pizza Delivery Race Understanding

    Two drivers deliver pizza to a house 10 km away.

    • Driver 1: Takes 10 minutes. Drives at a perfectly steady speed the whole way.
    • Driver 2: Drives 5 km in 5 minutes, stops for 2 minutes in traffic, then races the rest of the way.

    Which graph below matches Driver 2’s journey?

    A B

  9. Calculating Speed from a Graph Problem Solving

    The graph below shows a car journey. Use the values shown to calculate the car’s speed (Speed = Distance ÷ Time).

    2 hours 100 km
    1. What distance did the car travel?
    2. How long did the journey take?
    3. Calculate the car’s speed.

  10. Story Matching Problem Solving

    Story: “The temperature rose slowly during the morning, stayed the same all afternoon, then dropped quickly at night.”

    Which of the following graph shapes matches this story?

    1. Shape A: Steep Up → Flat → Gentle Down
    2. Shape B: Gentle Up → Flat → Steep Down

    State which shape matches, and explain why the other shape does not.

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