When you start learning about functions in Year 9, it's really important to know how linear functions are different from non-linear ones. Once you get this, math will start to make a lot more sense!

Linear Functions:

1. What They Are: Linear functions are shown by equations like $y = mx + b$. Here, $m$ is the slope, and $b$ is where the line crosses the y-axis (the y-intercept).

2. Graph Shape: The graphs of linear functions are straight lines. This makes it easier to see and guess what will happen next.

3. Changing Rate: The rate of change is steady. This means that when you increase $x$ by 1, $y$ changes by a set amount too.

4. Simple Examples: Picture saving money. If you save the same amount each week, that relationship is linear.

Non-Linear Functions:

1. What They Are: Non-linear functions don't make straight lines. They can look different, like quadratics ($y = ax^2 + bx + c$) or cubics ($y = ax^3 + bx^2 + cx + d$).

2. Graph Shape: Their graphs are curved, which can make them seem more complicated. They don’t have a steady slope!

3. Changing Rate: The rate of change can change a lot. For example, think about a ball being thrown in the air. It goes up and then comes down—that’s a non-linear relationship!

4. Simple Examples: Imagine a car speeding up. At first, it moves slowly, but then it goes faster and faster—this is definitely non-linear!

Knowing the differences between these functions will not only help you with graphing but also improve your problem-solving skills. Plus, it helps you see how math works in the world! Enjoy learning!