Question

How do you write `y - 4 = 2.5(x + 3)` 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 ensure all coefficients are integers:

`color(red)(2)(y - 4) = color(red)(2) xx 2.5(x + 3)`

`2y - 8 = 5(x + 3)`

Next, expand the terms on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`2y - 8 = color(red)(5)(x + 3)`

`2y - 8 = (color(red)(5)xx x) + (color(red)(5)xx 3)`

`2y - 8 = 5x + 15`

Then, add `color(red)(8)` and subtract `color(blue)(5x)` from each side of the equation to place the `x` and `y` terms on the left side of the equation and constant on the right side of the equation while keeping the equation balanced:

`-color(blue)(5x) + 2y - 8 + color(red)(8) = -color(blue)(5x) + 5x + 15 + color(red)(8)`

`-5x + 2y - 0 = 0 + 23`

`-5x + 2y = 23`

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

`color(red)(-1)(-5x + 2y) = color(red)(-1) xx 23`

`(color(red)(-1) xx -5x) + (color(red)(-1) xx 2y) = -23`

`color(red)(5)x - color(blue)(2)y = color(green)(-23)`