Question 1206810

Line {{{a}}}

{{{X}}}: {{{-11}}}, {{{-6}}},{{{ -1}}},{{{ 4}}}
{{{Y}}}: {{{81}}}, {{{51}}}, {{{21}}}, {{{-9}}}


{{{y=mx+b }}}


use two points to find a slope

({{{-1}}},{{{21}}}) and ({{{4}}},{{{-9}}})

{{{m=(-9-21)/(4-(-1))=-30/5=-6}}}

substitute in equation above

{{{y=-6x+b}}}...use one point to calculate {{{b}}}

{{{-9=-6*4+b}}}
{{{-9=-24+b}}}
{{{-9+24=b}}}
{{{b=15}}}

so, equation of the line {{{a}}} is

{{{y=-6x+15}}}

{{{highlight(6x+y=15)}}}


Line {{{b}}}
{{{X}}}: {{{-9}}}, {{{-4}}}, {{{1}}}, {{{6}}}
{{{Y}}}: {{{18}}}, {{{3}}}, {{{-12}}},{{{ -27}}}


{{{y=mx+b }}}

use two points to find a slope

({{{-9}}},{{{18}}}) and ({{{-4}}},{{{3}}})

{{{m=(3-18)/(-4-(-9))=-15/5=-3}}}

{{{y=-3x+b}}}...use one point to calculate{{{ b}}}

{{{3=-3*(-4)+b}}}
{{{3=12+b}}}
{{{3-12=b}}}
{{{b=-9}}}

so, equation of the line {{{b}}} is
{{{y=-3x-9}}}
{{{highlight(3x+y=-9)}}}


answer:

D) {{{6x + y = 15}}}, {{{3x + y = -9}}}