The goal in converting an equation to slopeintercept form is to isolate y on one side of the equation. Thus, to convert to slopeintercept form, perform inverse operations on variable terms and constant terms until y stands alone on one side.
Example: Convert
6y + 4x = 7
to slopeintercept form.
6y + 4x = 7
6y =  4x + 7
y = 
x +
y = 
x +
slopeintercept form
Slopeintercept form can be thought of as a specific case of pointslope form, in which the "point" is the y intercept. Thus, to convert to pointslope form, first convert to slopeintercept form, then move the constant term b to the left side of the equation (or isolate x and then divide by the y coefficient).
Example: Convert
3x = 4y + 8
to pointslope form.
3x = 4y + 8
3x  8 = 4y
x  = y
x  2 = y
y =
x  2
slopeintercept form
y + 2 =
x
pointslope form
The goal in converting an equation to general linear form is to place x and y on one side of the equation and convert all coefficients (and the constant term) to integers. Thus, to convert to general linear form, first isolate x and y on one side and the constant term on the other side. Next, if any of the coefficients are fractions, multiply the entire equation by the least common denominator of all the fractions.
Example: Convert
y + 1 = (x  2)
to general linear form.
y + 1 = (x  2)
y + 1 =
x 

x + y + 1 = 

x + y =   1

x + y = 
4(
x + y) = 4( )
5x + 4y =  14
general linear form