What is the standard form of ##y-7=-2/3 (x+1)##?

The standard form is the simplified form of that equation.

You first expand your right hand side: ##-2/3x - 2/3##

(Take note of the negative sign).

Then bring all to one side of the equation, bring them to the left. ## y-7+2/3x+2/3=0##.

Again take note how the negative sign changes. Finally you simplify ##y+2/3x-19/3=0 or y+2/3x=19/3##.

Then multiply by ##3## all through and you get, ##3y + 2x =19##