The above solution contains a sign error.

First we use the slope formula:

m = 
where (x1,y1) = (,).
and where (x2,y2) = (,-3).

m =  =  =  =  =  =  = 

Next we use the point slope formula: 

Point-slope formula:

y - y1 = m(x - x1)

where (x1,y1) = (,), m = 

y -  =  (x - )

y +  =  (x - )

Multiply through by 3

3y + 1 = 16(x - )

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) = (,). 

 = m + b

Simplify by multiplying through by LCD = 12

-4 = 3m + 12b

Substituting (x,y) = (,-3). 

-3 = m + 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

 = b

 = 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

 = m

 = m

So the equation in y-intercept form is

y = x +  

y = x -  

 3y = 16x - 5

-16x + 3y = -5

 16x - 3y = 5

Edwin