The parallel lines have the same a slope.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
P(0, 1), Q(5, 0). Substitute:
[tex]m_{PQ}=\dfrac{0-1}{5-0}=\dfrac{-1}{5}=-\dfrac{1}{5}[/tex]
R(-4, 3), S(-5, 4). Substitute:
[tex]m_{RS}=\dfrac{4-3}{-5-(-4)}=\dfrac{1}{-5+4}=\dfrac{1}{-1}=-1[/tex]
[tex]m_{PQ}\neq m_{RS}[/tex]
Therefore the lines PQ and RS are not parallel.
