When given an equation of a line an a point not on that line what are the steps to writing an equation that's through that point and parallel to that line?

If you represent the original straight line on a graph using Cartesian co-ordinates, it's equation will be y=mx+c where y and x are the variables and m and c are constants.

(m will equal the gradient of the line. c will be the point where the line cuts through the y axis).

Your new line, parallel to the original will be y=mx +c +d where d is the vertical distance between the point and the original line.