Question 1150511


the equation of the line:

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

given:
the line passes through ({{{-4}}},{{{k}}}) and ({{{-1}}}, {{{2k}}}) 

and have a y-intercept of {{{b=-7}}}

use given points to find a slope {{{m}}}

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}

{{{m=(2k-k)/(-1-(-4))}}}

{{{m=k/(-1+4)}}}

{{{m=k/3}}}

so far, your line is: {{{y=(k/3)x-7}}}

use one point and calculate {{{k}}}

{{{k=(k/3)(-4)-7}}}

{{{k=-(4k/3)-7}}}....both sides multiply by {{{3}}}

{{{3k=-4k-21}}}

{{{3k+4k=-21}}}

{{{7k=-21}}}

{{{k=-21/7}}}

{{{k=-3}}}

then, a slope is {{{m=k/3=-3/3=-1}}}

so, your equation is: {{{y=-x-7}}} 
and points are:  ({{{-4}}},{{{-3}}}) and ({{{-1}}}, {{{-6}}})


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(-4,-3,.12),circle(-1,-6,.12),
locate(-4,-3,p(-4,-3)),locate(-1,-6,p(-1,-6)),
graph( 600, 600, -10, 10, -10, 10, -x-7)) }}}