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
$(0,b)$.
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.