<PRE><B>Question 330383</B>
&lt;br&gt;In order to figure this out, just find out the slope of each line by putting the original equations in slope-intercept form! &lt;br&gt;

4x+3y=2&lt;br&gt;

3y=-4x+2&lt;br&gt;

y=-4x/3+2/3&lt;br&gt;

Thus, the slope of the first line is -4/3&lt;br&gt;

4x+3y=10&lt;br&gt;

3y=-4x+10&lt;br&gt;

y=-4x/3+10/3&lt;br&gt;

Thus, the slope of the second line is -4/3&lt;br&gt;

It is then easy to see that the 2 lines have the same slope, but different y-intercepts.&lt;br&gt;

When 2 lines have the same slope, but are not the same line, by definition, they are parallel lines!&lt;br&gt;

If the slopes of the 2 lines were negative reciprocals of each other, ie slope1=-1/slope2, then the lines would be perpendicular to each other.&lt;br&gt;

Otherwise, the 2 lines are neither parallel nor perpendicular to each other.&lt;br&gt;

I hope this helps!  :)</PRE>