Question 662747
{{{slope-intercept}}} form: {{{y=mx+b}}} where {{{m}}} is a slope and {{{b}}} is {{{y-intercept}}}.

{{{3x+4y=4}}}

{{{4y=-3x+4}}}

{{{y=-(3/4)x+4/4}}}

{{{y=-(3/4)x+1}}}...so, the slope is {{{m[1]=-(3/4)}}} and {{{y-intercept}}} is

 {{{b=1}}}


{{{-8+6y=0}}}

{{{6y=0+8}}}

{{{6y=8}}}

{{{y=8/6}}}

{{{y=4/3}}}.......so, the slope is {{{m[2]=0}}} and {{{y-intercept}}} is  

{{{b=4/3}}}


compare slopes: we have {{{m[1]=-(3/4)}}} and {{{m[2]=0}}}


{{{m[1]<>m[2]}}}


since parallel lines have same slope, and our slopes are not equal, means our lines are not parallel

since perpendicular lines have a slope that is the {{{inverse}}} and {{{opposite}}} of the line to which it is perpendicular, {{{m[1]=-1/m[2]}}} and in our case it is {{{-(3/4)<>-1/0}}}, means our lines are not perpendicular either

so, answer is: our lines are  neither parallel nor perpendicular


let's see it on a graph:

{{{ graph( 600, 600, -10, 10, -10, 10, -(3/4)x+1,4/3) }}}