Question 1011494

on the graph we have two points and we can use them to find the equation of the line passing through these two points

points:

({{{-2}}},{{{3}}}) and ({{{-1}}},{{{-4}}}) 

the equation of the line written in slope-intercept form is:

{{{y=mx+b}}} where {{{m}}} is a slope and {{{b}}} is y-intercept

use the points to find {{{m}}}  and {{{b}}}

{{{y=mx+b}}} for ({{{-2}}},{{{3}}})

{{{3=m(-2)+b}}}

{{{3=-2m+b}}}...solve for {{{b}}}

{{{b=2m+3}}}.........eq.1



{{{y=mx+b}}} for ({{{-1}}},{{{-4}}})

{{{-4=m(-1)+b}}}

{{{-4=-m+b}}}

{{{b=m-4}}}..........eq.2

since left sides of eq.1 and eq.2 same, equal right sides

{{{2m+3=m-4}}}

{{{2m-m=-4-3}}}

{{{highlight(m=-7)}}}

go to {{{b=m-4}}}..........eq.2, substitute {{{-7}}} for {{{m}}}

{{{b=-7-4}}}

{{{highlight(b=-11)}}}

so, your equation is: {{{highlight(y=-7x-11)}}}