Parallel lines have the same slope, so the slope must be (1-4)/(2-(-3))=-3/5.
Now we plug (-1,3) into the slope-intercept equation: y-3=(-3/5)(x-(-1)), y-3=(-3/5)(x+1), y=-⅗x-⅗+3, y=-⅗x+12/5. This can be written y=⅗(4-x), 5y=12-3x, 3x+5y=12 or 3x+5y-12=0.