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.