Question 1076932

 Find an equation for the line perpendicular to the line {{{4x + 20y = 6 }}}

equation of the perpendicular line:
{{{y=mx+b}}}
if given that  the line perpendicular to the line {{{4x + 20y = 6 }}}, means they will have slopes negative reciprocal to each other

so, first find a slope of given line:
 {{{4x + 20y = 6 }}}
 {{{ 20y = -4x+6 }}}
 {{{ y = -(4/20)x+6/20 }}}
{{{ y = -(1/5)x+3/10 }}}=> slope is {{{m=-(1/5)}}}

and its negative reciprocal will be a slope of the  perpendicular line:

if {{{m=-(1/5)}}}, than negative reciprocal is {{{-1/(-(1/5))}}}=>{{{5}}}

now we have a slope, and your equation is {{{y=5x+b}}} so far

since given that perpendicular line  having the same y-intercept as {{{-5x - 7y = 56 }}}, we need to find that   y-intercept

{{{-5x-56 = 7y }}}

{{{y=-(5/7)x - 56/7 }}}
{{{y=-(5/7)x -8 }}}=> y-intercept is at {{{b= -8}}}

so, your equation is:{{{y=5x-8}}}


{{{ graph( 600, 600, -10, 10, -10, 10, 5x-8, -(1/5)x+3/10) }}}