The "cook-book" way:

To get the left side of the equation

1. Swap the coefficients of x and y

2x,3y

2. Change the sign of the coefficient of y

2x,-3y

3. Write them added together with an equal sign after them

2x-3y =

4. Substitute the point, x=4, y=-2

2(4)-3(-2)
8+6
14

5. Put that number on the right side (after the equal sign)

2x-3y = 14  

It's like magic! No thinking required. Just memorize how to do it.

Edwin