Question

How do you write `y = 7/2x – 6` 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

First, multiply both sides of the equation by `color(red)(2)` to eliminate the fraction while keeping the equation balanced. The standard form of a linear equation must have coefficients which are integers.

`color(red)(2) xx y = color(red)(2)(7/2x - 6)`

`2y = (color(red)(2) xx 7/2x) - (color(red)(2) xx 6)`

`2y = (cancel(color(red)(2)) xx 7/color(red)(cancel(color(black)(2)))x) - 12`

`2y = 7x - 12`

Next, subtract `color(red)(7x)` from each side of the equation to move the `x` term to the left side of the equation while keeping the equation balanced. The standard form of a linear equation has the `x` and `y` terms on the left side of the equation.

`-color(red)(7x) + 2y = -color(red)(7x) + 7x - 12`

`-7x + 2y = 0 - 12`

`-7x + 2y = -12`

Now, multiply each side of the equation by `color(red)(-1)` to put the equation in standard form while keeping the equation balanced. In a standard form linear equation the coefficient of the `x` term should be a positive integer.

`color(red)(-1)(-7x + 2y) = color(red)(-1) xx -12`

`(color(red)(-1) xx -7x) + (color(red)(-1) xx 2y) = 12`

`color(red)(7)x - color(blue)(2)y = color(green)(12)`