Question 80715
You can do this by finding the slopes {{{m = (y[2]-y[1])/(x[2]-x[1])}}} of the two lines.
If the slopes are equal, the lines are parallel, if the slopes are the negative reciprocal of each other, the lines are perpendicular. 
L1:
{{{m[1] = (3-(-7))/(1-(-4))}}}
{{{m[1] = (3+7)/(1+4)}}}
{{{m[1] = 10/5}}}
{{{m[1] = 2}}}
L2:
{{{m[2] = (10-6)/(4-2)}}}
{{{m[2] = 4/2}}}
{{{m[2] = 2}}}  

As you can see, the slopes are equal so this means that the lines are parallel!