Question

How do you write `y = 4 x – 7` 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)(4x)` from each side of the equation to place both the `x` and `y` variables on the left side of the equation as required by the formula:

`-color(red)(4x) + y = -color(red)(4x) + 4x - 7`

`-4x + y = 0 - 7`

`-4x + y = -7`

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

`color(red)(-1)(-4x + y) = color(red)(-1) xx -7`

`(color(red)(-1) xx -4x) + (color(red)(-1) xx y) = 7`

`color(red)(4)x + color(blue)(-1)y = color(green)(7)`

Or

`color(red)(4)x - color(blue)(1)y = color(green)(7)`

Or

`color(red)(4)x - y = color(green)(7)`