Question 1139235
to find the equation of the straight line that passes through points ( {{{-3}}} ,{{{ 1}}} ) and ( {{{1}}},{{{ -1 }}}), first use given points to calculate a slope

{{{m=(y[2]-y[1])/ (x[2]-x[1])}}}.......plug in given coordinates


{{{m=(-1-1)/ (1-(-3))}}}


{{{m=-2/ (1+3)}}}

{{{m=-2/4}}}

{{{m=-1/2}}}


now use point slope formula:

{{{y-y[1]=m(x-x[1])}}}...plug in a slope and coordinates of one point

{{{y-(-1)=-(1/2)(x-1)}}}

{{{y+1=-(1/2)x+1/2}}}

{{{y=-(1/2)x+1/2-1}}}

{{{y=-(1/2)x-1/2}}}-> your answer


check:

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(1,-1,.12),locate(1,-1,p(1,-1)),
circle(-3,1,.12),locate(-3,1,p(-3,1)),
 graph( 600, 600, -10, 10, -10, 10, -(1/2)x-1/2)) }}}