Answer:
The first pair of lines is neither perpendicular not parallel. The second pair of lines is parallel.
Step-by-step explanation:
If a line is defined as
[tex]Ax+By+C=0[/tex]
Therefore the slope of the line is
[tex]m=\frac{-A}{B}[/tex]
Slope of parallel lines are equal. Product of slopes of perpendicular lines is -1.
In the first pair of lines,
[tex]y=3x+5[/tex]
It is a slope intercept form of a line, therefore the slope of the line is 3.
[tex]-3x-y=9[/tex]
This equation can be written as
[tex]0=9+3x+y[/tex]
Slope of the line is
[tex]m=\frac{-3}{1}=-3[/tex]
The slopes of both lines are not equal therefore the lines are not parallel. The product of their slopes is not -1, therefore the lines are not perpendicular.
In the second pair of lines,
[tex]y-7x=3[/tex]
This equation can be written as
[tex]y-7x-3=0[/tex]
Therefore the slope of the line is
[tex]m=\frac{7}{1}=7[/tex]
[tex]14x-2y=28[/tex]
This equation can be written as
[tex]14x-2y-28=0[/tex]
[tex]m=\frac{-14}{-2}=\frac{7}{1}=7[/tex]
Since the slopes of lines are equal, therefore the lines are parallel to each other.
