Question

It passes through (-1,4) and is perpendicular to the x axis

Answer 1

line x=4 is perpendicular to x-axis. So line, which is perpendicular to x=4 line, will be parallel to x-axis, therefore it is perpendicular to y-axis. Line, which is parallel to x-axis, has zero slope. Its equation, therefore, is y=0x+b or simply y=b. Since it shall pass through point (1,-4), its coordinates must satisfy the line equation. x does not matter, since there is no x in equation y=b, thus only y-coordinate matters. Plug in -4 into the equation, to obtain -4=b. So y=-4 is your answer.  Answer: y=-4