Question 6348
write an equation of a line given (x1,y1)=(12,7) and (x2,y2)=(-4,5)

   {{{m = (y2-y1)/(x2-x1)}}}

   {{{m = (5-7)/(-4-12)}}}

   {{{m = (-2)/(-16)}}}

   {{{m = 1/8}}}

Now use

{{{y-y1 = m(x-x1)}}}

 {{{y-7 = (1/8)(x-12)}}}

 {{{y-7 = (1/8)x-3/2}}}

   {{{y = (1/8)x-3/2 + 7}}}

   {{{y = (1/8)x-3/2 + 14/2}}}

   {{{y = (1/8)x+ 11/2}}}

That will do as a final answer if you only want the slope-intercept
form, or,
you can multiply through by 8 and get rid of fractions

  {{{8y = x + 44}}}

and to get it in standard form Ax + By = C

  {{{-x + 8y = 44}}}

and since the standard form requires that A be positive,
we multiply thru by -1

  {{{x - 8y = -44}}}

Edwin