|x   y   1|
|4  -2   1| = 0
|1   3   1|
========
x*(-2*1 - 3*1) - y*(4*1 - 1*1) + 1*(4*3 - 1*-2) = 0
-5x - 3y + 14 = 0

First, calculate the slope.


    The formula for the slope of a straight line passing through two given points  (,)  and  (,)  is
        m = .

    Substitute the given data   = 4,   = -2,   = 1,  = 3  into the basic formula

        m =  =  = .


Next, write an equation of the line having the slope    and passing through the given point (4,-2).


    An equation of a straight line in a coordinate plane which has the slope m and passes through the given point  P = (a,b)  is 

        y - b = m*(x-a).     

    Substitute here  m = ,  a = 4,  b = -2,  and you will get

        y - (-2) = ,   or, equivalently,


        y + 4    = .


        Having the equation in this form, you can convert it to any other equivalent form you want.