(i) Given:
[tex]x=2,y=-5[/tex]
These two lines are straight lines and perpendicular to each other.
(ii) Given:
[tex]\begin{gathered} y=7x \\ y-28=7(x-4) \end{gathered}[/tex]
Since the slope of both equations is the same (m=7).
Hence, the lines are parallel.
(iii) Given:
[tex]\begin{gathered} y=2x-1 \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]
The slope of the first equation is 2.
The slope of the second equation is 1/2.
Since they are neither parallel nor perpendicular.
Hence, the answer is neither.
(iv)Given:
[tex]\begin{gathered} y-3=\frac{1}{4}(x-3) \\ y+13=\frac{1}{4}(x+1) \end{gathered}[/tex]
Since the slope of both equations is the same.
That is,
[tex]m=\frac{1}{4}[/tex]
Hence, the lines are parallel.
