How to identify the kind of relationship in a graph

Graphs represent different types of relationships between variables. The shape of the graph helps determine the type of relationship.

1. Linear Graphs (Straight Line Graphs)

Not in Proportion

• A straight-line graph that can be increasing or decreasing.
• Not necessarily proportional.

Direct Proportion

• A straight-line graph that starts at (0,0).
• Always increasing.
• Both quantities increase in the same proportion.

2. Inverse Proportion (Curved Graphs)

• Curved graph that does not touch the axes.
• As one quantity increases, the other decreases.
• Example: Speed vs. Time for a fixed distance.

3. Exponential Growth Graphs

• Curved graph that increases steeply over time.
• Touches the vertical axis at the starting point.
• The vertical quantity grows faster and faster.
• Example: Compound interest or population growth.