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
First, we will multiply each side of the equation by color(red)(6) to eliminate the fractions because by the definition above all of the coefficients and the constant must be integers:
color(red)(6) * y = color(red)(6)(-3/2x + 4/3)
6y = (color(red)(6) xx -3/2x) + (color(red)(6) xx 4/3)
6y = (cancel(color(red)(6))3 xx -3/color(red)(cancel(color(black)(2)))x) + (cancel(color(red)(6))2 xx 4/color(red)(cancel(color(black)(3))))
6y = -9x + 8
Now, we will add color(red)(9x) to each side of the equation to put this equation into standard form:
color(red)(9x) + 6y = color(red)(9x) - 9x + 8
9x + 6y = 0 + 8
color(red)(9)x + color(blue)(6)y = color(green)(8)
