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, expand the terms in parenthesis:
y - 3 = (-2.4 xx x) + (2.4 xx 5)
y - 3 = -2.4x + 12
Next, add color(red)(3) and color(blue)(2.4x) to each side of the equation to move towards the standard form while keeping the equation balanced:
color(blue)(2.4x) + y - 3 + color(red)(3) = color(blue)(2.4x) - 2.4x + 12 + color(red)(3)
2.4x + y - 0 = 0 + 15
2.4x + y = 15
Now, we multiply each side of the equation by color(red)(5) to convert all coefficients to integers while keeping the equation balanced:
color(red)(5)(2.4x + y) = color(red)(5) xx 15
(color(red)(5) xx 2.4x) + (color(red)(5) xx y) = 75
color(red)(12)x + color(blue)(5)y = color(green)(75)
