Linear equations can be transformed by changing either the x -coefficient or the constant term.
Use this applet to see the effect of each change and relate this to a linear equation in the form y =mx + c
Turn the trace on to see copies of the line when you move the slider.

Note in these examples of Linear Equations y is the subject of the equation. This is called the "slope intercept" form of a linear equation must be written with just y on the left hand side.
The same is true for linear functions - f(x) =mx + c - this is essentially the same as above but just uses a different notation.