Question 58519
Well, first off, to determine if two lines are parallel, they would have the same slope.  If they are perpendicular, the slopes would be opposite (i.e. a slope of 2 and a slope of 1/2 are perpendicular).  So you have to put these equations in slope-intercept form. 

-4x + 3y = 4
<u>+4x &nbsp&nbsp&nbsp&nbsp +4x</u>&nbsp&nbsp&nbsp&nbsp&nbspAdd 4x to both sides
<u>3y</u>&nbsp=&nbsp<u>4x</u>&nbsp+&nbsp<u>4</u>&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbspDivide by 3
   3&nbsp&nbsp&nbsp&nbsp&nbsp3&nbsp&nbsp&nbsp&nbsp&nbsp3
y = 4/3x + 4/3  This is your first equation



-8x + 6y = 0 
<u>+8x&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp+8x</u>&nbsp&nbsp&nbsp&nbsp&nbspAdd 8x to both sides
<u>6y</u> = <u>8x</u>&nbsp&nbsp&nbsp&nbsp&nbspDivide by 6
6&nbsp&nbsp&nbsp&nbsp&nbsp6
y = 8/6x&nbsp&nbsp&nbsp&nbsp&nbspSimplify
y = 4/3x&nbsp&nbsp&nbsp&nbsp&nbspThis is your second equation

Note what I said above and take that into account.  Both of the slopes are 4/3x, which means that the lines are <b>parallel</b>!