Question 850858
<pre>
First we use the slope formula:

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

where (x<sub>1</sub>,y<sub>1</sub>) = (-8, 2) 

and where (x<sub>2</sub>,y<sub>2</sub>) = (5, -7).

m = {{{((-7)-(2))/((5)-(-8))}}}

m = {{{(-7-2)/(5+8)}}}

m = {{{(-9)/13}}} = {{{-9/13}}}

Then we use the point-slope formula:

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

where (x<sub>1</sub>,y<sub>1</sub>) = (-8, 2)

and m = {{{-9/13}}}

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

y - 2 = {{{-9/13}}}(x - (-8))

y - 2 = {{{-9/13}}}(x + 8)

Multiply both sides by 13 to clear the fraction:

13(y - 2) = 13·{{{-9/13}}}(x + 8) 

13y - 26 = -9(x + 8)

13y - 26 = -9x - 72

9x + 13y = -46  < -- that's standard form.

or solve for y:

     13y = -9x - 46

     {{{13y/13}}} = {{{-9/13}}}x - {{{46/13}}}

     y = {{{-9/13}}}x - {{{46/13}}}   < --- that's slope intercept form.

Edwin</pre>