Gradients are really important for understanding how function graphs work.

The gradient, or slope, tells us how steep a line is on a graph. There are different types of gradients:

1. Positive Gradient:

   • This happens when the graph goes up from left to right.
   • It shows that when one thing (the independent variable, $x$) increases, the other thing (the dependent variable, $y$) also goes up.
   • For example, in the line equation $y = mx + b$, if $m$ is greater than 0, like in $y = 2x + 3$, the slope is positive and is 2.

2. Negative Gradient:

   • This occurs when the graph goes down from left to right.
   • It means that when $x$ increases, $y$ decreases.
   • For instance, in the line $y = -mx + b$ with $m$ being more than 0, like in $y = -3x + 4$, the slope is -3, showing a negative gradient.

3. Zero Gradient:

   • This is found in straight, horizontal lines.
   • It means that $y$ doesn't change even when $x$ does; the line stays the same.
   • An example is the line $y = 5$, which has a gradient of 0.

4. Undefined Gradient:

   • This type happens in straight, vertical lines.
   • It means that $x$ stays the same while $y$ changes.
   • For instance, the line $x = 3$ has an undefined gradient because it doesn’t have a slope.

By understanding these different gradients, students can read and create function graphs better. This helps them see and understand the relationships and behaviors in math, especially in the British Year 10 curriculum.