Question 1113172
equation in slope-intercept form: {{{y=mx+b}}} where {{{m}}} is a slope and {{{b}}} is y-intercept

Line 1
{{{x}}}|{{{y}}}
{{{-2}}}|{{{4}}}
{{{2}}}|{{{6}}}
	
{{{y=mx+b}}} ...use given {{{x}}} and {{{y}}} to find {{{m}}} and {{{b}}}

if {{{x=-2}}} and {{{y=4}}}, we have

{{{4=-2m+b}}} ...solve for {{{b}}}

{{{b=4+2m}}}....eq.1


if {{{x=2}}} and {{{y=6}}}, we have

{{{6=2m+b}}} ...solve for {{{b}}}

{{{b=6-2m}}}....eq.2

since eq.1 and eq.2 have same left sides, right sides must be equal too; so, we have

{{{4+2m=6-2m}}}...solve for {{{m}}}

{{{2m+2m=6-4}}}

{{{4m=2}}}

{{{m=2/4}}}

{{{m=1/2}}}

{{{highlight(m=0.5)}}}

go back to eq.1, plug in {{{m}}}

{{{b=4+2m}}}....eq.1
{{{b=4+2*0.5}}}
{{{b=4+1}}}
{{{highlight(b=5)}}}

so, Line 1: {{{y =  0.5x +5}}}

 

Line 2


 {{{x}}}|{{{y}}}
{{{-2}}}|{{{-2}}}
{{{0}}}|{{{0}}} -> this shows you that line 2 passes through origin; so, y-intercept {{{highlight(b=0)}}}

use that and other given {{{x}}} and {{{y}}} values to find {{{m}}}

{{{-2=-2m+0}}} ...solve for {{{m}}}	

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

{{{highlight(m=1)}}}

so, Line 2: {{{y = x }}}