parallel means has the same slope
to find the slope
m = (y2 - y2)/ (x2 - x1)
m =( -3 - 1) / (2 - 4)
m = -4/-2
m = 2
The equation is
y = mx + b
y = 2x + b
to find the y-intercept, plug in the given coordinate
-1 = 2(1) + b
-1 = 2 + b
subtract 2 from both sides
-3 = b
The equation for the line that passes through (1,-1) and is parallel to the line through (4,1) and (2,-3) is
y = 2x - 3
Hope this helps