Question 1134566

a general linear equation: ​{{{Ax+By+C=0}}}

passes through ({{{-4}}},{{{5}}}) and ({{{3}}},{{{8}}}) 


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

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

{{{m=(8-5)/(3-(-4))}}}

{{{m=(8-5)/(3+4)}}}

{{{m=3/7}}}


now use point slope form to find equation:


{{{y-y[1]=m(x-x[1])}}}...plug in {{{m}}} and coordinates of the point ({{{-4}}},{{{5}}})

{{{y-5=(3/7)(x-(-4))}}}

{{{y-5=(3/7)(x+4)}}}

{{{y-5=3x/7+12/7}}}............both sides multiply by {{{7}}}

{{{7y-35=3x+12}}}

{{{-3x+7y-35-12=0}}}

{{{-3x+7y-47=0}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,

circle(-4,5,.12),locate(-4,5,p(-4,5)),
circle(3,8,.12),locate(3,8,p(3,8)),
graph( 600, 600, -10, 10, -10, 10, (3/7)(x+4)+5)) }}}