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
To convert to Standard Form for a linear equation, first, subtract color(red)(1/4x) from each side of the equation to put the x and y variables both on the left side of the equation while keeping the equation balanced:
-color(red)(1/4x) + y = -color(red)(1/4x) + 1/4x + 3
-1/4x + y = 0 + 3
-1/4x + y = 3
Now, multiply each side of the equation by color(red)(-4) to eliminate the fraction and to ensure the x coefficient is positive while keeping the equation balanced:
color(red)(-4)(-1/4x + y) = color(red)(-4) xx 3
(color(red)(-4) xx -1/4x) + (color(red)(-4) xx y) = -12
(cancel(color(red)(-4)) xx 1/color(red)(cancel(color(black)(-4)))x) - 4y = -12
color(red)(1)x - color(blue)(4)y = color(green)(-12)
