Question

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

Answer 1

`2x+3y=4`

Explanation:

We have:

`y-2=-2/3(x+1)`

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(y-2)=-2(x+1)`

Distribute out the brackets:

`3y-6=-2x-2`

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

`2x+3y=4`

Let's check this by graphing both forms. This is `y-2=-2/3(x+1)`:

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

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

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