Question 159308
Let's find the slope of the first line.
Convert to slope-intercept form , {{{y=mx+b}}}
{{{3x-4y=2}}}
{{{-4y=2-3x}}}
{{{y=(3x-2)/4}}}
{{{y=(3/4)x-1/2}}}
The slope of the first line is {{{m[1]=3/4}}}
Convert the second equation to slope-intercept form , {{{y=mx+b}}}
{{{Ax+By=13}}}
{{{By=13-Ax}}}
{{{y=13/B-(A/B)x}}}
But you know B=2
{{{y=13/2-(A/2)x}}}
The slope of the second line is 
{{{m[2]=-(A/2)}}}
Perpendicular line have the property that their slopes are negative reciprocals of each other. 
{{{m[1]m[2]=-1}}}
{{{(3/4)(-A/2)=-1}}}
{{{A=8/3}}}
We can plot both lines to check the answer and perpendicularity. 
{{{drawing( 300, 300, -2, 10, -2, 10,grid( 1 ),graph( 300, 300, -2, 10, -2, 10, (3/4)x-1/2, 13/2-(4/3)x)))}}})