Question 115008
Parallel lines have the same slope. 
Perpendicular lines have slopes that are negative reciprocals of each other.
Put both equations into the slope intercept form. 
Small problem, L1 is not an equation, there is no equal sign. 
I'll assume you meant like this.
L1 : {{{x-2y=10}}}
L2 : {{{2x+y=2}}}
The answer will be the same since the constant has no effect on slope. 
For line 1,
L1:{{{x-2y=10}}}
{{{-2y=10-x}}}
{{{y=-5+x/2}}}
{{{y=x/2-5}}}
{{{m[1]=1/2}}}
For line 2, 
L2 : {{{2x+y=2}}}
{{{y=-2x+2}}}
{{{m[2]=-2}}}
Since {{{m[1]=-1/m[2]}}}, the slopes are negative reciprocals of each other. 
The lines are perpendicular to each other.

{{{ graph( 300, 300, -10, 10, -10, 10, -2x+2, x/2-5) }}}