How do I write y-3=2/3 (x-2) in standard form

To write y-3=2/3 (x-2), you must change the equation to this format: ax+by=c, whereas there are no common factors between the coefficients and constant, no fractions or decimals, and the coefficient of a cannot be negative. To start, first multiple both sides by 3 to get rid of the fraction 2/3. This would result in this: 3y-9=2 (x-2)

Then, you distribute the 2 to (x-2) and you get 3y-9=2x-4

Now, to get this equation into ax+by=c form, subtract 2x from both sides, and add 9 to both sides, which will result in this: - 2x+3y=5.

Now, since the coefficient of a is negative, multiply the entire equation by - 1, to get you answer: 2x-3y=-5