This is the eqn of a str line. y+4=12/7(x-1) would be clearer if written as
y+4=(12/7)(x-1). y+4 = (12/7)x - 12/7.
Multiply all terms by 7 to remove the fractions: 7(y+4) = 12x - 12.
Complete the multiplication: 7y + 28 = 12x - 12.
Arrange the x and y terms on the left side and the constants on the right:
-12x + 7y = -40. This is standard form. Some people might disagree and say that -12x + 7y + 40 is standard form. They are equivalent.