Question

How do you write `y=x/3-6` in standard form?

Answer 1

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

The first step is to multiple each side of the equation by `color(red)(3)` to obtain all integers:

`color(red)(3) xx y = color(red)(3) xx (x/3 - 6)`

`3y = (color(red)(3) xx x/3) - (color(red)(3) xx 6)`

`3y = (cancel(color(red)(3)) xx x/color(red)(cancel(color(black)(3)))) - 18`

`3y = x - 18`

Next step is to move `x` to the left side of the equation by subtracting `color(red)(x)` from each side of the equation:

`-x + 3y = 0 - 18`

`-x + 3y = -18`

Now we can multiply each side of the equation by `color(red)(-1)` to make the coefficient of `x` positive. The coefficient is `-1` currently.

`color(red)(-1) xx (-x + 3y) = color(red)(-1) xx -18`

`x - 3y = 18`

or

`color(red)(1)x - color(blue)(3)y = color(green)(18)`