Duration: 45 minutes
By the end of this lesson, you will be able to:
Do you remember plotting points?
Example: Point (2, 3)
Graphs use coordinates to show information!
A distance-time graph shows:
It's a picture of a journey!
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)
Think about it:
It's natural and logical!
A matatu traveling from Kampala:
How can we show this on a graph?
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!
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)
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!
We can read information from our graph:
Read across from time, up from distance
The straight line means:
Straight line = constant speed
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
New scenario - a cyclist's journey:
Notice something different at hour 3?
Distance (km) 60 | • 40 | _____• 20 | • 0 | •____________→ Time (hours) 0 1 2 3 4
See the horizontal line from 2 to 3 hours?
Horizontal line = RESTING
Between hours 2 and 3:
Time continues, but distance doesn't increase
Important concept:
This is why horizontal means rest!
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!
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
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!
Example: Walk from home to market and back
Total distance traveled = 10 km, not back to 0!
Look at this graph and answer:
Distance (km) 80 | • 60 | ___• 40 | • 20 | • 0 |____________→ Time (hours) 0 1 2 3 4
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?
Distance-Time Graphs show journeys visually
Graphs help us:
A picture is worth a thousand words!
Distance-time graphs are used for:
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!
Assignment:
Draw axes for a distance-time graph:
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
Explain: What does a horizontal line mean on a distance-time graph? Why?
Expected time: 25 minutes
Tomorrow we will:
Bring your ruler, pencil, and exercise book!
Created: January 11, 2026 Based on: NCDC P6 Mathematics Curriculum - Topic 8: Distance, Time and Speed
Source: National Curriculum Development Centre (NCDC), Uganda