Question 1009214


What is the equation of the line 
passing through ({{{-2}}},{{{6}}}) 
with the x-intercept half the y-intercept? 

{{{y=mx+b }}} where {{{m=slope}}} and {{{b=y-intercept}}} and we need to find that

use given point ({{{-2}}},{{{6}}})

{{{6=m(-2)+b }}}
{{{6=-2m+b }}}.......solve for {{{b}}}
{{{b=2m+6}}}............eq.1

 the x-intercept is where {{{y=0}}}

so, {{{0=mx+b}}}............solve for {{{x}}}

 {{{x= -b/m}}}...........eq.2

if the x-intercept is {{{half}}} the y-intercept, then {{{x=b/2}}}

so, we have

{{{b/2= -b/m}}} 

{{{mb=-2b}}}

{{{highlight(m= -2)}}}

go back to {{{b=2m+6}}}............eq.1, substitute {{{m}}} and solve for {{{b}}}

{{{b=2(-2)+6}}}

{{{b=-4+6}}}

{{{b=2}}}

and, your equation is: {{{y= -2x+2 }}}

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-2,6,.12),locate(-2,6,p(-2,6)),
 graph( 600, 600, -10, 10, -10, 10, -2x+2)) }}}