Linear relations > Linear functions
1234Linear functions

## Theory

Take a look at the applet: Linear Function

If $y$ is a linear function of $x$ then the corresponding formula can be written as $y=a\cdot x+b$, where

• $a$ is the gradient, that is the increase (decrease) of $y$ per unit step $x$;

• $b$ is the y-intercept, the value of the function if $x=0$.

The graph of such a linear relationship is a straight line through $\left(0,b\right)$.
If you then increase the value of $x$ by $1$, the function value will increase (or decrease) by $a$.
The gradient $a$ is also called the slope, because this number determines the direction of the line.