Gradient as a rate
A graph shows taxi cost rises from £0 to £24 over 3 hours. What is the cost per hour?
- Cost per hour is total cost divided by hours.
- 24 divided by 3 = 8
Answer: The gradient means £8.00 per hour.
Back to National 5
Topic
Graphs and Relationships
Graphs and relationships uses real-life graphs to read values, compare rates, and explain what a gradient means in context.
Topic explanation
Always read the axis labels before answering. A graph might show cost, distance, time, temperature, or another real quantity.
Gradient is not just a number. In context it might mean cost per hour, speed, or amount used per day.
A graph can tell a story. Rising, falling, flat, and steep sections each need to be interpreted in the situation given.
For scattergraphs, describe the correlation and use the line of best fit only as an estimate. Do not claim that one variable definitely causes the other.
Quick methods
- Read values
- Use the axes and scale carefully.
- Compare
- Look at which graph is higher or steeper.
- Gradient
- Gradient means rate of change in the context.
- Flat section
- A flat distance-time graph means no movement.
Worked examples
Flat section
A distance-time graph is flat for 20 minutes. What does this mean?
- A flat section means the distance is not changing.
- If distance is not changing, the person is stopped.
So: The person stopped moving for 20 minutes.
Compare steepness
Plan A increases by £12 per month. Plan B increases by £18 per month. Which graph is steeper?
- Steeper means a larger increase for each month.
- £18 is larger than £12.
Final step: Plan B has the steeper graph.
Graph interpretation
A water tank graph rises quickly for 10 minutes, then rises more slowly for the next 20 minutes. What does this suggest?
- A rising graph means the amount of water is increasing.
- A steeper section means a faster rate.
- The later section is less steep, so the tank is filling more slowly.
Answer: The tank is still filling, but at a slower rate after the first 10 minutes.
Watch out: A less steep rising graph does not mean the amount is falling.