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 per unit step ;
$b$ is the y-intercept, the value of the function if $x=0$.
The graph of such a linear relationship is a straight line through $(0,b)$.
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.