how would you find an equation to a line that is parallel and 3 units away from the line x-5y+10=0?
The equation of the original line can be written in standard form
y = (x/5) + 2
Any parallel line will be of the form
y = (x/5) + b
where b is any constant.
Let the difference between the y-intercepts be C. If parallel lines are to be separated by 3, a bit of geometry results in
(3)^2 + (3/5)^2 = C^2
C^2 = 9.36
C = 3.059 (rounded off)
There are two parallel lines spaced 3 units away, one above and one below. Their equations are
y = (x/5) + 5.059, and
y = (x-5) - 1.059