Question

How do you write `y + 1 = x + 2` in standard form?

Answer 1

See a solution process below:

Explanation:

The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

First, subtract `color(red)(1)` and `color(blue)(x)` from each side of the equation to have the `x` and `y` term on the left side of the equation and the constant on the right side as required by the Standard Form for a linear equation while keeping the equation balanced:

`-color(blue)(x) + y + 1 - color(red)(1) = -color(blue)(x) + x + 2 - color(red)(1)`

`-x + y + 0 = 0 + 1`

`-x + y = 1`

Now, multiply each side of the equation by `color(red)(-1)` to transform the coefficient of the `x` variable to a positive integer as required by the Standard Form for a linear equation while keeping the equation balanced:

`color(red)(-1)(-x + y) = color(red)(-1) * 1`

`(color(red)(-1) * -x) + (color(red)(-1) * y) = -1`

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

`color(red)(1)x - color(blue)(1)y = color(green)(-1)`