A line L is parallel to y = 4x+5 and passes through the point (-1,6). Find the equation of the line L in the form y = ax+b.

If line L is parallel to line A it will have the same gradient; in this case, the letter a in the equation y=ax+b represents the gradient. Therefore line L will be of the form y=4x+b. To find the value of b, we know that it passes through the co-ordinates (-1, 6) so we must insert these into our new equation. Doing so gives us: 6=4(-1)+b. Once we expand the brackets this becomes: 6=-4+b. In order to get the value b by itself on the right-hand side of the equation, we must add 4 to both sides which gives us: 10=b. Now we have the value of b, we can insert this into the basic equation we had earlier which was: y=4x+b. So the equation of line L must be: y=4x+10.