We are given the equation:
4 x - y = -2
and asked to find the equation of a lie perpendicular to it from the given options.
So we need to find the slope of the given equation in order to be able to answer. We isolate y on one sid, to be able to identify the slope of the given line:
4 x + 2 = y
then, y = 4 x + 2 which tells us that the slope of the given line is "4"
We know that a line perpendicular to one of slope "4" must be of the form: "- 1/4"
then, the only possible option is the second one listed, that clearly gives "- 1/4" as the slope of the line.
We select then the second option: y = - 1/4 - 3 as our sought line.
