When you look at graphs of linear and non-linear functions, it's like stepping into two different worlds!

1. Linear Functions: Linear functions are like the straight lines of the graphing universe! They can be written with the formula $y = mx + b$. Here, $m$ is the slope (how steep the line is) and $b$ is where the line crosses the y-axis. When you plot these, you get a straight line.

This line changes at a steady rate. For example, if you look at the function $y = 2x + 3$, every time you go one step to the right on the x-axis, the y value goes up by the same amount.

2. Non-Linear Functions: On the other hand, non-linear functions, like quadratic ones, mix things up! You can write them with the formula $y = ax^2 + bx + c$. When you graph these, you get curves instead of straight lines.

For example, with $y = x^2$, you get a U-shaped curve called a parabola. As you move along this graph, the changes in the y value start small but then get much bigger as the x value increases.

Comparison:

• Shape: Linear functions create straight lines, while non-linear functions create curves.

• Rate of Change: In linear functions, the change is steady; in non-linear functions, it changes in different ways.

• Real-Life Examples: Think of a straight road (linear) compared to a roller coaster track (non-linear).

Knowing the differences between these two types of functions helps us understand and predict things in the real world—not just in math. It opens up new ways to see patterns and connections!