Question 1198524


 the line passing through ​({{{-2}}}​,{{{6}}}​) and parallel to{{{ x+3y=5}}}

 parallel lines have same slope

so
{{{ x+3y=5}}}......write in slope-intercept form
{{{ 3y=-x+5}}}
{{{ y=-(1/3)x+5/3}}}

=> the slope is {{{m=-(1/3)}}}


​(a) in​ slope-intercept form 

{{{y=mx+b}}}
{{{y=-(1/3)x+b}}}.........use given point to calculate {{{b}}}
{{{6=-(1/3)(-2)+b}}}
{{{6=2/3+b}}}
{{{6-2/3=b}}}
{{{b=16/3}}}

your equation is

{{{y=-(1/3)x+16/3}}}

(b) in standard form

{{{y=-(1/3)x+16/3}}}..........both sides multiply by {{{3}}}

{{{3y=-x+16}}}
{{{x+3y=16}}}


{{{ drawing( 600, 600, -10, 10, -10, 10, 
circle(-2,6,.12),locate(-2,6,p(-2,6)),
graph( 600, 600, -10, 10, -10, 10, -(1/3)x+5/3, -(1/3)x+16/3) )}}}