Write the standard form of the equation y+4=12/7 (x-1)

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.