Question

find the equation of the lines making an angle of tan^-1(3) with the line 2x-y-8=0 and passing through (4,-1)

Answer 1

y = 2x - 8 has slope 2 nad lakes an angle of 63.4 degrees with horizontal
the other line will make angle tan-1(3) = 71.6 to this line
that is 135 degrees to horizontal which is a slope of -1 (tan 135 = -1)

it also goes through the point (4,-1) so using the standard form
y-y=m(x-x1) we have

y-(-1) = -1(x - 4)
y + 1 = -x + 4
y + x = 3

Answer 2

Thank you for your help, it is very much appreciated.