The linear equation is the simplest form of equation you may deal with; it restricts the problem to a unique unknown variable (usually called x) and no exponent (e.g. f(x) = 2x + 15).

The general form of such an equation is: $$\textbf{f(x) = ax + b}$$

Any linear expression can be drawn as a line in a 2D graphic. The graph drawing is straightforward: we have y, or f(x), on the vertical axis (the result) and for a range of x values (horizontal abscissa) we compute and plot the points (x, y).

The easiest line, a constant: y=-3 (for all x: y = -3).

The other basic line to know: y=x (for all x, y as the same value).

Drawing here y = 2x
Multiplying x by a constant is making a rotation on the line.

Drawing here all together y = 2x - 3
Adding or subtracting the expression by a constant value is just adding an offset.

In brief:
Changing a is changing the slope of the line.
Changing b is changing the offset of the line.