The gradient of a function shows how much the output changes when the input changes. Here’s how to understand it:

1. Formula:
   To find the gradient (slope) between two points, $(x_1, y_1)$ and $(x_2, y_2)$, use this formula:

   $$\text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1}$$

2. What It Means:

   • A positive gradient means the function is going up.
     For example, if the gradient is 2, that means when $x$ goes up by 1, $y$ goes up by 2.
   • A negative gradient means the function is going down.
     For instance, if the gradient is -3, when $x$ goes up by 1, $y$ goes down by 3.

3. Real-Life Example:
   In a straight-line equation, $y = mx + c$, the letter $m$ shows the gradient. This number tells you how fast the function changes.

By understanding the gradient, you can see how different inputs will affect the output in a function!