Question 727411
<pre>
The above solution contains a sign error.

First we use the slope formula:

m = {{{(y[2]-y[1])/(x[2]-x[1])}}}
where (x<sub>1</sub>,y<sub>1</sub>) = ({{{1/4}}},{{{-1/3}}}).
and where (x<sub>2</sub>,y<sub>2</sub>) = ({{{-1/4}}},-3).

m = {{{((-3)-(-1/3))/((-1/4)-(1/4))}}} = {{{(-3+1/3)/(-1/4-1/4)}}} = {{{-3/1+1/3)/(-2/4)}}} = {{{(-9/3+1/3)/-1/2)}}} = {{{(-8/3)/(-1/2)}}} = {{{expr(-8/3)*expr(-2/1)}}} = {{{16/3}}}

Next we use the point slope formula: 

Point-slope formula:

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

where (x<sub>1</sub>,y<sub>1</sub>) = ({{{1/4}}},{{{-1/3}}}), m = {{{16/3}}}

y - {{{-1/3}}} =  {{{16/3}}}(x - {{{1/4}}})

y + {{{1/3}}} =  {{{16/3}}}(x - {{{1/4}}})

Multiply through by 3

3y + 1 = 16(x - {{{1/4}}})

3y + 1 = 16x - 4

-16x + 3y = -5

Multiply through by -1

16x - 3y = 5

-------------------------------------

Here is another way to do it:

Substitute both points in 

y = mx + b

Substituting (x,y) = ({{{1/4}}},{{{-1/3}}}). 

{{{-1/3}}} = m{{{(1/4)}}} + b

Simplify by multiplying through by LCD = 12

-4 = 3m + 12b

Substituting (x,y) = ({{{-1/4}}},-3). 

-3 = m{{{(-1/4)}}} + b

Simplify by multiplying through by LCD = 4

-12 = -m + 4b

So you have the system of equations:

 -4 = 3m + 12b
-12 = -m +  4b

Multiply the bottom equation through by 3 to make the m
terms cancel, then add the equations term by term:

 -4 =  3m + 12b
-36 = -3m + 12b
---------------
-40 =       24b

{{{-40/24}}} = b

{{{-5/3}}} = b

 -4 = 3m + 12b
-12 = -m +  4b

Multiply the bottom equation through by -3 to make the b
terms cancel, then add the equations term by term:

 -4 = 3m + 12b
 36 = 3m - 12b
---------------
 32 = 6m

{{{32/6}}} = m

{{{16/3}}} = m

So the equation in y-intercept form is

y = {{{16/3}}}x +  {{{-5/3}}}

y = {{{16/3}}}x -  {{{5/3}}}

 3y = 16x - 5

-16x + 3y = -5

 16x - 3y = 5

Edwin</pre>