Question 939515
linear equation is: {{{y=mx+b}}} where {{{m}}} is a slope and {{{b}}} is a y-intercept; so, we need {{{m}}}  and {{{b}}}

Determine the equation of  

from the graph we see that the line passing through points  C =({{{2}}},{{{-2}}}) and D=({{{4}}},{{{0}}}) which means:

if {{{x=2}}} => {{{y=-2}}}
and 
if {{{x=4}}} => {{{y=0}}}=> a x-intercept {{{highlight(x=4)}}}

then we will use these points to set the system of  two equations to find {{{m}}}  and {{{b}}}

{{{y=mx+b}}} ........if {{{x=2}}},{{{y=-2}}} we have

{{{-2=m*2+b}}} ........eq.1


{{{y=mx+b}}} ........if ({{{4}}},{{{0}}}) we have

{{{0=m*4+b}}} ........eq.2

solve the system:

{{{-2=2m+b}}} ........eq.1
{{{0=4m+b}}} ........eq.2
----------------------------------------------subtract eq.1 from eq.2
{{{0-(-2)=4m+b-2m-b}}} 

{{{2=2m}}} 

{{{m=2/2}}}

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

now find {{{b}}}

{{{0=4m+b}}} ........eq.2

{{{0=4*1+b}}}

{{{0=4+b}}}

{{{-4=b}}}

{{{highlight(b=-4)}}}

so, your equation is:  {{{y=x-4}}} 

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(2,-2,.13),circle(4,0,.13),
locate(2,-2,C(2,-2)),locate(4,0.6,D(4,0)),
 graph( 600, 600, -10, 10, -10, 10, x-4)) }}}