Direct Proportion

Direct proportion occurs when two quantities increase or decrease at the same rate. If you double one, the other doubles as well.

The Mathematical Formula

The relationship is expressed as: $$y = kx$$

Where:

• $y$ and $x$ are the variables.
• $k$ is the constant of proportionality.

Key Characteristics

1. The ratio $\frac{y}{x}$ is always constant ($k$).
2. The graph is always a straight line passing through the origin (0,0).

Example

If 5 apples cost $10, how much do 8 apples cost?

1. Find $k$: $\frac{10}{5} = 2$. (Each apple costs $2).
2. Apply to new value: $y = 2 \times 8 = 16$. Answer: $16.