Positive and negative gradients in function graphs show us how the function is changing.

1. Positive Gradient:

   • A positive gradient means the function is going up.
   • For example, if the gradient between two points is $m = \frac{1}{2}$, it means that for every step up in $x$, $y$ goes up by $0.5$.
   • This tells us that things are growing or getting bigger.

2. Negative Gradient:

   • A negative gradient means the function is going down.
   • For instance, if the gradient is $m = -1$, it means that for every step up in $x$, $y$ goes down by $1$.
   • This shows that things are falling or getting smaller.

To find the gradient, we use this formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$.

This formula helps us calculate how steep the graph is!