So,
Two lines are parallel when their slopes are the same.
So, let's find the slope of each line, and then compare them.
[tex]\begin{gathered} L_1\colon(x_1,y_1)=(2,-1);\text{ }(x_2,y_2)=(5,-7) \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Replacing the ordered pairs in the equation, we obtain:
[tex]m=\frac{-7-(-1)}{5-2}=\frac{-6}{3}=-2[/tex]Thus the slope of the first line is -2. Let's use the same process to find the slope of the second line:
[tex]L_2\colon(x_1,y_1)=(0,0);\text{ }(x_2,y_2)=(-1,2)[/tex]Given:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\to m=\frac{2-0}{-1-0}=\frac{2}{-1}=-2[/tex]As you can see, the slope of both lines is the same. So, the lines are parallel.
