Introduction to Graphs
Focused last-minute revision with key concepts, formulas, worked examples, exam traps and practice.
Chapter Snapshot
- The horizontal axis is x and the vertical axis is y.
- The axes meet at the origin (0,0).
- Coordinates are written x first, y second.
- A graph turns numerical relationships into visual patterns.
- A straight line often represents a constant rate in simple situations.
What You Will Learn
- Identify axes and origin
- Read ordered pairs correctly
- Plot points
- Interpret line graphs
- Plot simple relationships from tables
Last-Minute Chapter Map
Use this chapter in three passes:
- Understand the core ideas.
- Memorise formulas and exam traps.
- Attempt the compact practice set without looking at the answers.
Coordinate plane
Two perpendicular number lines form the Cartesian plane. The horizontal line is the x-axis, the vertical line is the y-axis and their intersection is the origin.
Ordered pairs
A point is written as (x,y). Read the x-coordinate first, then the y-coordinate.
Plotting from a table
Create ordered pairs from matching values in a table, plot them using the chosen scale, then join points only when the relationship meaningfully continues between them.
Reading graphs
Always check title, axis labels, units and scale. Then read the required coordinate, trend or rate.
Simple linear graphs
Relationships such as y=3x give points that lie on a straight line because y changes at a constant rate with x.
Coordinates are always written in the order x then y.
Worked Examples
The point is (5,10).
Exam Traps
Quick Revision
Quick Revision
- The horizontal axis is x and the vertical axis is y.
- The axes meet at the origin (0,0).
- Coordinates are written x first, y second.
- A graph turns numerical relationships into visual patterns.
- A straight line often represents a constant rate in simple situations.
Compact Practice
Origin coordinates?
View Solution
(0,0)
x-coordinate of (4,-2)?
View Solution
4
Which axis is vertical?
View Solution
y-axis
For y=3x, what point corresponds to x=4?
View Solution
(4,12)
Final Chapter Summary
Chapter Summary
- The horizontal axis is x and the vertical axis is y.
- The axes meet at the origin (0,0).
- Coordinates are written x first, y second.
- A graph turns numerical relationships into visual patterns.
- A straight line often represents a constant rate in simple situations.
- Prioritise correct method, clean working and final units where applicable.