SOLUTION: find the standard form for the equation of the line qhich passes through the point (-1,2) and is parallel to the line that has an equation of 6x+2y=4

Solve that for y

    2y = -6x + 4

Divide every number by 2, the coefficient of y:

   y = x + 

     y = -2x + 2

Compare that to

     y =  mx + b

Then m = -2 and b = 2.   We don't need b, we just need m

m is the slope of the line which is the graph of the given equation.
Namely this one:



It's slope is -2, we can tell it has a slope which is a negative number
because the line goes downhill to the right. We can tell it has slope -2
because it drops 2 units for every 1 unit it moves to the right.

We want the equation of a line that passes through the point (-1,2)
and is parallel to the green one, like this red one:



To do that we use the point-slope form for the equation of a line, which is

     y - y1 = m(x - x1)

and we substitute m = -2, x1 = -1, y1 = 2

     y - 2 = -2[x - (-1)]

     y - 2 = -2[x + 1]

     y - 2 = -2x - 2

         y = -2x  
   

Edwin