Algebra: Slopes of Parallel and Perpendicular

Question

How to write an equation of the line passing through the point (-4,1) passing through parallel to x+4y+3 and perpendicular to x+4y+3?

Answer 1

parallel to x+4y + 3 = 0 means slope of -1/4

perpendicular to the same line is impossible as its slope would be 4 and -1/4 at the same time

but to calculate a line through (-4,1) with either

would be

y-1 = 4(x+4) = 4x +16

y = 4x + 1

or

y -1 = (-1/4)(x+4)

y =-x/4 -1 +1 = -x/4

y = -x/4

so depending on what you really asked, the answer looks like eitther

y =-x/4

or

y =-4x + 1

One of the two