Question 57665
Parallel means the lines have an identical slope (m).  Perpendicular means the lines have slopes that are the negative reciprocals of each other (so, if the slope of one line is 2, the slope of its perpendicular line is -1/2).  Anything else means the lines intersect at an angle other than 90.

To solve these, write the equations in slope-intercept form and you can solve by inspection.

Problem 1:
eq(1): 2x+5y=-8
eq(2): 6+2x=5y

eq(1) leads to: {{{y=-(2/5)x-(8/5)}}}, so the slope (m) is -2/5
eq(2) leads to: {{{y=(2/5)x+(6/5)}}}, so the slope (m) is 2/5

Because the slopes are not the same or the negative reiprocals of each other, they are neither parallel nor perpendicular.

Here is a graph showing them:
{{{graph(300,200,-10,10,-10,10,-(2/5)x-(8/5), (2/5)x+(6/5))}}}

The second problem can be solved the same way.  The slopes are 3 and 3, which are the same therefore the lines are parallel.