Question

How do you write `y = 1/2x-1` 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, multiply each side of the equation by `color(red)(2)` to eliminate the fraction and ensure all of the coefficients are integers as required by the formula while keeping the equation balanced:

`color(red)(2) * y = color(red)(2)(1/2x - 1)`

`2y = (color(red)(2) * 1/2x) - (color(red)(2) * 1)`

`2y = 2/2x - 2`

`2y = 1x - 2`

Next, subtract `color(red)(1x)` from each side of the equation so the `x` and `y` terms are on the left side of the equation while keeping the equation balanced:

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

`-1x + 2y = 0 - 2`

`-1x + 2y = -2`

Now, multiply each side of the equation by `color(red)(-1)` to make the `x` coefficient non-negative as required by the formula while keeping the equation balanced:

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

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

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

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