Introduction to Distance-Time Graphs

Lesson 5 of 6: Distance, Time and Speed

In this lesson:

• Read values from a distance-time graph
• Understand what straight and horizontal lines mean
• Connect the graph to the speed formula

What You Will Learn Today

By the end of this lesson:

1. Explain what a distance-time graph shows
2. Identify time on x-axis, distance on y-axis
3. Read distance and time values from a graph
4. Understand that a straight line means constant speed
5. Recognize a horizontal line as rest (no movement)
6. Explain why distance does not decrease on this graph

What If We Graphed a Journey?

You know coordinates: (2, 3) means 2 right, 3 up.

New question: What if one axis showed time and the other distance?

• Horizontal axis → Time (hours)
• Vertical axis → Distance (km)

Each point: at this time, the traveller was this far from the start.

The Distance-Time Graph: Axes Setup

Reading Coordinates: Each Point Tells a Story

Each point = (time, distance)

• (1, 30): 1 hour → 30 km from start
• (2, 60): 2 hours → 60 km from start
• (3, 90): 3 hours → 90 km from start

Always read time first, then distance.

Matatu Journey: Reading the Graph

A matatu travels from Kampala. Read each point: (1, 30), (2, 60), (3, 90)

Quick Check: Reading the Matatu Graph

From the graph:

• What is the distance after 2 hours?
• What is the speed of the matatu for this journey?

Read the graph, then apply the speed formula.

Quick Check: Reading the Graph — Answers

• After 2 hours: 60 km (read from graph at time = 2)

• Speed:

Or: 30 km every hour, readable directly from the graph.

Straight Line = Constant Speed

A straight line on a distance-time graph means constant speed.

• Equal distance covered in equal time periods
• 30 km every hour → straight line
• If speed changed, the line would curve or change slope

Faster and Slower: Comparing Two Lines

Steeper line = more distance in same time = faster speed

Quick Check: Steeper Means Faster

Two lines on a distance-time graph. Line A is steep. Line B is gentle.

• Which represents the faster traveller?
• How do you know — in terms of distance and time?

Answer in full before advancing.

Quick Check: Which Line Is Faster?

Line A (steep) is the faster traveller.

Why: steeper slope = more distance covered per hour = higher speed.

Steeper ≠ slower. Steeper = more distance in same time = faster.

Horizontal Line: The Traveller Is Resting

From time 2 to 3: distance stays at 60 km — the traveller is resting.

Time Goes On, Distance Stays the Same

During rest:

• Time continues to increase (x-axis value increases)
• Distance does not change (y-axis value stays constant)

Horizontal line → speed =

Journey with Rest: Read the Graph

From the graph with the rest period:

1. What is the distance at time = 3 hours?
2. What graph feature shows the traveller is resting?

Answer both before advancing.

Journey with Rest: Graph Answers

• At time 3: distance = 60 km (same as at time 2 — no change)

• The horizontal section (flat line from 2 to 3) shows the traveller is resting.

The graph shows: moving → resting → moving again.

Practice: Read the Assessment Graph

Points: (0, 0), (1, 20), (2, 60), (3, 60), (4, 80)

1. Distance at 1 hour?
2. Distance at 2 hours?
3. What happened between hours 2 and 3?
4. Total distance at 4 hours?
5. Speed for first 2 hours?
6. Which axis shows time?

Answer all six.

Practice: Check All Six Answers

1. 20 km
2. 60 km
3. Resting — distance stayed at 60 km (horizontal section)
4. 80 km
6. Horizontal axis (x-axis)

Key Rules for Distance-Time Graphs

✓ Time → x-axis (horizontal) · Distance → y-axis (vertical)

✓ Read coordinates as (time, distance) — not the other way round

✓ Straight line → constant speed · Steeper = faster

Horizontal line = resting (time goes on, distance does not)

Line never goes down — distance is from starting point

Steeper ≠ slower — steeper always means faster

Next Lesson: Plot Your Own Graph

In Lesson 6, you will:

• Create your own distance-time graph from a data table
• Plot points accurately on scaled axes
• Interpret a complex journey with multiple sections

Homework: Draw axes (time 0–4 hr, distance 0–80 km). Plot: (0,0), (1,15), (2,30), (3,30), (4,50). What happened at hour 3?