Question

How do you write `y - 2 = - 1/2 (x - 4)` in standard form?

Answer 1

See the entire 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

To start, multiply each side of the equation by `color(red)(2)` to eliminate the fraction and keep the equation balanced:

`color(red)(2)(y - 2) = color(red)(2) xx -1/2(x - 4)`

`(color(red)(2) xx y) - (color(red)(2) xx 2) = -color(red)(2)/2(x - 4)`

`2y - 4 = -1(x - 4)`

`2y - 4 = (-1 xx x) - (-1 xx 4)`

`2y - 4 = -1x - (-4)`

`2y - 4 = -1x + 4`

Now, add `color(blue)(4)` and `color(red)(1x)` to each side of the equation to put the `x` and `y` terms on the left side of the equation and the constant on the right side of the equation while keeping the equation balanced:

`color(red)(1x) + 2y - 4 + color(blue)(4) = color(red)(1x) - 1x + 4 + color(blue)(4)`

`color(red)(1x) + 2y - 0 = 0 + 8`

`color(red)(1)x + color(blue)(2)y = color(green)(8)`