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)#
