Question 658972
 Since slopes of perpendicular lines are negative reciprocals of each other,

first find a slope of the line {{{-4x-8y=3}}}

use the {{{slope-intercept}}} form {{{y=mx+b}}} where {{{m}}} is a slope and {{{b}}} is {{{y-intercept}}}


{{{-4x-3=8y}}}


{{{-(4/8)x-3/8=y}}}


{{{y=-(1/2)x-3/8}}}.....as you can see {{{m=-(1/2)}}} and {{{b=-3/8}}}

now, let {{{y=m[1]x+b[1]}}} be a line that is perpendicular on given line


if {{{m=-(1/2)}}}, then negative reciprocals of it is {{{m[1]=-(1/(-1/2))}}}

{{{highlight(m[1]=2)}}}

 since given that new line has the same {{{y-intercept}}} as {{{6x-4y=-6}}}, means {{{b[1]}}} will be:

{{{6x-4y=-6}}}...first solve for {{{y}}}

{{{6x+6=4y}}}

{{{6x/4+6/4=y}}}

{{{y=(3/2)x+3/2}}}....=>...{{{highlight(b[1]=3/2)}}} 

now, our line is:

{{{highlight(y=2x+3/2)}}}

let's see our line on a graph:


{{{ graph( 600, 600, -10,10, -10, 10, 2x+3/2) }}}


now, check if this line is perpendicular to {{{-4x-3=8y}}}:


{{{ graph( 600, 600, -10,10, -10, 10, 2x+3/2,-(1/2)x-3/8) }}}


now check if our line has same {{{y-intercept}}} as {{{6x-4y=-6}}}:


{{{ graph( 600, 600, -10,10, -10, 10, 2x+3/2,(3/2)x+3/2) }}}