Question 1176537
Point-slope is the general form {{{y-y₁=m(x-x₁) }}}for linear equations.

given:

Passing through ({{{-5}}}, {{{-3}}}) and ({{{-3}}}, {{{-8}}})

find a slope first:

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

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

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

{{{m=-5/2}}}


{{{y-y₁=-(5/2)(x-x₁) }}}..........use one point

{{{y-(-3)=-(5/2)(x-(-5)) }}}

{{{y+3=-(5/2)(x+5) }}}

{{{y+3=-(5/2)x-(5/2)5 }}}

{{{y=-(5/2)x-25/2-3 }}}

{{{y=-(5/2)x-25/2-6/2 }}}

{{{y=-(5/2)x-31/2 }}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(-5,-3,.12), circle(-3,-8,.12),
locate(-5,-3,p(-5,-3)),locate(-3,-8,p(-3,-8)),
graph( 600, 600, -10, 10, -10, 10,-(5/2)x-31/2  )) }}}