What's the difference between linear and non-linear patterns?

📚 Linear Patterns Explained

A linear pattern is like a straight line. Imagine a plant growing the same amount every day. That consistent growth represents a linear pattern. Mathematically, it follows a simple formula where the rate of change is constant.

📈 Non-Linear Patterns Explained

A non-linear pattern is like a curve or wave. Think about the spread of a virus – it starts slow, then explodes, then slows down again. This kind of growth is not constant. The rate of change varies, creating a curve when graphed.

Feature	Linear Pattern	Non-Linear Pattern
Definition	Forms a straight line when graphed.	Forms a curve or other non-straight shape when graphed.
Rate of Change	Constant (the same throughout).	Varies (changes over time).
Formula	Typically represented by a linear equation, such as $y = mx + b$.	Represented by non-linear equations, such as quadratic ($y = ax^2 + bx + c$) or exponential equations ($y = a^x$).
Example	Simple interest earned on a fixed amount.	Compound interest earned on an investment.
Graph	Straight Line	Curve (parabola, exponential curve, etc.)

🔑 Key Takeaways

• 📏Straight vs. Curved: Linear patterns create straight lines; non-linear patterns create curves.
• 🔄Constant vs. Variable: The rate of change is constant in linear patterns but varies in non-linear ones.
• 🧮Equations: Linear patterns follow linear equations (like $y = mx + b$), while non-linear patterns follow equations with exponents or other non-linear operations (like $y = x^2$).