# Put y-2=-2/3(x+1) into standard form?

$2 x + 3 y = 4$

#### Explanation:

We have:

$y - 2 = - \frac{2}{3} \left(x + 1\right)$

and we want to put it into a form that looks like:

ax+by=c; a, b, c in ZZ - or in other words, no fractions.

We can do this by first multiplying both sides by 3 to get rid of the denominator on the right side:

$3 \left(y - 2\right) = - 2 \left(x + 1\right)$

Distribute out the brackets:

$3 y - 6 = - 2 x - 2$

Let's now move the $x$ term to the left hand side and the constants to the right:

$2 x + 3 y = 4$

Let's check this by graphing both forms. This is $y - 2 = - \frac{2}{3} \left(x + 1\right)$:

graph{y-2=-2/3(x+1) [-10, 10, -5, 5]}

and this is $2 x + 3 y = 4$:

graph{2x+3y-4=0 [-10, 10, -5, 5]}