Question

How do you write `y=3x+1` in standard form using integers?

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)(3x)` from each side of the equation to place the `x` and `y` terms on the left side of the equation as required by the definition:

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

`-3x + y = 0 + 1`

`-3x + y = 1`

Now, multiply each side of the equation by `color(red)(-1)` to make the `x` coefficient positive as required by the definition:

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

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

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