The standard form of a linear equation is:
color(red)(A)x + color(blue)(B)y = color(green)(C)
where, if at all possible, color(red)(A), color(blue)(B), and color(green)(C)are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
We can transform to this form as follows:
y + 3 = (3 xx x) - (3 xx 2)
y + 3 = 3x - 6
y + 3 - color(red)(3) - color(blue)(3x) = 3x - 6 - color(red)(3) - color(blue)(3x)
- color(blue)(3x) + y + 3 - color(red)(3) = 3x - color(blue)(3x) - 6 - color(red)(3)
-3x + y + 0 = 0 - 9
-3x + y = -9
color(red)(-1)(-3x + y) = color(red)(-1) xx -9
(color(red)(-1) xx -3x) + (color(red)(-1) xx y) = 9
color(red)(3)x - color(blue)(1)y = color(green)(9)
