Introduction to Distance-Time Graphs
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P6 Mathematics - Term II

Topic 8: Distance, Time and Speed

Lesson 5: Introduction to Distance-Time Graphs

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

  • Understand what a distance-time graph shows
  • Identify the axes on a distance-time graph
  • Read distance and time values from a graph
  • Recognize that a straight line means constant speed
  • Understand that a horizontal line means rest
  • Know that distance does not decrease on these graphs

Review: Coordinates

Do you remember plotting points?

Example: Point (2, 3)

  • Move 2 steps right on x-axis
  • Move 3 steps up on y-axis
  • Mark the point

Graphs use coordinates to show information!

What is a Distance-Time Graph?

A distance-time graph shows:

  • How far someone or something has traveled (distance)
  • At different points in time
  • As a visual line or curve

It's a picture of a journey!

The Axes

Every distance-time graph has two axes:

Distance (km)
↑
|
|
|____________→ Time (hours)

Time is ALWAYS on the horizontal axis (x-axis)
Distance is ALWAYS on the vertical axis (y-axis)

Why Time is on the X-Axis

Think about it:

  • Time moves forward (left to right)
  • We read time like we read words (left to right)
  • As time passes, we move across the graph

It's natural and logical!

A Simple Journey: Data Table

A matatu traveling from Kampala:

Time (hours) Distance (km)
0 0
1 30
2 60
3 90

How can we show this on a graph?

Drawing the Graph: Step 1 - Axes

First, draw and label the axes:

Distance (km)
100 |
 80 |
 60 |
 40 |
 20 |
  0 |___|___|___|___→ Time (hours)
    0   1   2   3   4

Label both axes with units!

Drawing the Graph: Step 2 - Plot Points

Plot each coordinate from the table:

Distance (km)
100 |              •
 80 |          •
 60 |      •
 40 |
 20 |  •
  0 |•___|___|___|___→ Time (hours)
    0   1   2   3   4

(0,0), (1,30), (2,60), (3,90)

Drawing the Graph: Step 3 - Join Points

Connect the points with straight lines:

Distance (km)
100 |              •
 80 |          •
 60 |      •
 40 |  •
 20 |•
  0 |_______________→ Time (hours)
    0   1   2   3   4

Use a ruler for straight lines!

Reading the Graph

We can read information from our graph:

  • At time 0: distance = 0 km (starting point)
  • At time 1 hour: distance = 30 km
  • At time 2 hours: distance = 60 km
  • At time 3 hours: distance = 90 km

Read across from time, up from distance

What Does the Line Tell Us?

The straight line means:

  • The matatu travels at constant speed
  • Same distance covered each hour (30 km per hour)
  • No stopping or slowing down
  • Speed = 30 km/hr throughout

Straight line = constant speed

Calculating Speed from the Graph

We can find speed from the graph:

In 1 hour: 30 km traveled
Speed = Distance ÷ Time
Speed = 30 ÷ 1 = 30 km/hr

Or:

In 3 hours: 90 km traveled
Speed = 90 ÷ 3 = 30 km/hr

A Journey with Rest

New scenario - a cyclist's journey:

Time (hours) Distance (km)
0 0
1 20
2 40
3 40
4 60

Notice something different at hour 3?

Graphing the Cyclist's Journey

Distance (km)
60 |                  •
40 |          _____•
20 |      •
 0 |  •____________→ Time (hours)
   0   1   2   3   4

See the horizontal line from 2 to 3 hours?

What Does a Horizontal Line Mean?

Horizontal line = RESTING

Between hours 2 and 3:

  • Distance stays at 40 km (doesn't change)
  • Time continues (from 2 to 3)
  • The cyclist is resting or stopped
  • Speed = 0 km/hr during rest

Time continues, but distance doesn't increase

Understanding Rest on Graphs

Important concept:

  • Time ALWAYS continues (left to right on graph)
  • Distance only increases when moving
  • When resting: time passes, distance stays same
  • Result: horizontal line

This is why horizontal means rest!

Comparing Graph Sections

Cyclist's journey in three parts:

Part 1 (0-2 hours): Slanted line up = traveling at 20 km/hr
Part 2 (2-3 hours): Horizontal line = resting, speed 0
Part 3 (3-4 hours): Slanted line up = traveling at 20 km/hr

Different parts of journey, different graph shapes!

Fast vs Slow on Graphs

Steeper line = faster speed

Distance (km)        Fast
60 |              •
40 |          •      Slow
20 |      •  •
 0 |  •  •________→ Time
   0  1  2  3  4

The steeper the line, the faster the speed

Important Rule: Distance Never Decreases

On a distance-time graph:

✅ Distance can stay the same (horizontal - resting)
✅ Distance can increase (slanted up - traveling)
❌ Distance NEVER decreases (no downward lines)

Why? Distance is measured from starting point!

Why No Downward Lines?

Example: Walk from home to market and back

  • Home to market: 5 km (distance = 5 km)
  • At market: rest (distance = 5 km)
  • Return home: walk another 5 km (distance = 10 km total)

Total distance traveled = 10 km, not back to 0!

Practice: Reading a Graph

Look at this graph and answer:

Distance (km)
80 |              •
60 |          ___•
40 |      •
20 |  •
 0 |____________→ Time (hours)
   0  1  2  3  4
  1. What is the distance after 1 hour?
  2. When did the person rest?
  3. What is the total distance after 4 hours?

Answers: Reading the Graph

1. Distance after 1 hour = 20 km
   (Read across from 1, up to line)

2. Rested between 2 and 3 hours
   (Horizontal line)

3. Total distance after 4 hours = 80 km
   (Read across from 4, up to line)

How did you do?

Summary: Key Concepts

Distance-Time Graphs show journeys visually

  • Time: horizontal axis (x-axis)
  • Distance: vertical axis (y-axis)
  • Straight slanted line: constant speed
  • Horizontal line: resting (speed = 0)
  • Steeper line: faster speed
  • Distance never decreases

Why Graphs Are Useful

Graphs help us:

  • See the whole journey at once
  • Identify rest periods easily
  • Compare speeds visually
  • Understand patterns in motion
  • Present information clearly

A picture is worth a thousand words!

Real-Life Applications

Distance-time graphs are used for:

  • Tracking vehicles and deliveries
  • Planning journey schedules
  • Analyzing sports performance (running, cycling)
  • Understanding traffic patterns
  • Science experiments about motion

Common Mistakes to Avoid

Don't do these:

❌ Put distance on x-axis and time on y-axis
❌ Forget to label axes with units
❌ Draw curved lines instead of straight ones
❌ Think horizontal means not moving in time
❌ Draw lines going downward

✅ Time on x, distance on y, straight lines, label everything!

Homework

Assignment:

  1. Draw axes for a distance-time graph:

    • Label horizontal axis: Time (hours) from 0 to 4
    • Label vertical axis: Distance (km) from 0 to 80
  2. Study this data and answer:

    Time (hours):  0    1    2    3    4
    Distance (km): 0   15   30   30   50
    

    a) What is the distance after 1 hour?
    b) What happened between 2 and 3 hours?
    c) Calculate the speed during the first 2 hours
    d) Calculate the speed between 3 and 4 hours

  3. Explain: What does a horizontal line mean on a distance-time graph? Why?

Expected time: 25 minutes

Next Lesson Preview

Tomorrow we will:

  • Plot our own distance-time graphs from data
  • Create complete graphs step by step
  • Interpret complex journeys with multiple parts
  • Calculate speeds from different sections
  • Solve problems using graphs

Bring your ruler, pencil, and exercise book!

Credits

Created: January 11, 2026
Based on: NCDC P6 Mathematics Curriculum - Topic 8: Distance, Time and Speed

Source: National Curriculum Development Centre (NCDC), Uganda