Question 105681
Line l goes through (1,3).
Line 1 is parallel to the line through (4,3) and (-3,1)
Let's call that line 2.
First, let's find the slope of line 2. 
Then, we'll find the equation for line 1. 
The slope of a line through two points is given by the formula:
{{{m=(y[2]-y[1])/(x[2]-x[1])}}}
In your case,
{{{m[2]=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m[2]=(1-3)/(-3-4)}}}
{{{m[2]=(-2)/(-7)}}}
{{{m[2]=2/7}}}
Parallel lines have the same slope. 
{{{m[1]=m[2]=2/7}}}
The slope-intercept form of the line is 
{{{y=mx+b}}}
Since line 1 goes through (1,3), we can use that information to solve. 
{{{y=mx+b}}}
{{{3=2/7*(1)+b}}}
{{{b=3-2/7}}}
{{{b=21/7-2/7}}}
{{{b=19/7}}}
{{{y=(2/7)x+19/7}}}
Here's how it all looks graphically. 
{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  blue(circle( 4, 3, .15 )),
  red(circle( 1, 3, .15 )),
  blue(circle(-3, 1, .15 )),
  blue(line( 4, 3, -3, 1 )),
  red(line( -10, -.14, 10, 5.57 ))
)}}}