Question

Determine whether the graphs of the given pair of lines are parallel perpendicular or neither.

Answer 1

Parallel lines have the same slope.  Perpendicular lines have reciprocal negative slopes (1/4 and -4, for example)
1) Put the second in y =mx+b form (m is the slope, so you can compare)
-x+4y =0 
+x
4y=x+0
Divide 4y=1/4+0
4 and 1/4 are not the same or negative reciprocals so it is neither.

2)Put the second in y=mx+b form.
2x+y =7
-2x
y= -2x +7
-2 and -2 are the same so the lines are parallel.

3) Both are already in slope-intercept form (y=mx+b)
1 and -1 (place 1 in front of the x's) are negative reciprocals.  They are perpendicular.