how to write an equation in standard form

Writing an equation in standard form is a way to express the equation of a line in a specific, standardized format. The standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants and x and y are variables. Here are some tips on how to write an equation in standard form:

Simplify the equation. To write an equation in standard form, it is important to simplify it as much as possible. Move any variables to one side of the equation and all constants to the other side.

Ensure the coefficients are integers. The coefficients A, B, and C must be integers, so if any fractions or decimals are present, they must be converted to integers.

Make sure A is positive. The coefficient A must be positive, so if it is negative, multiply both sides of the equation by -1 to make it positive.

Write the equation in the form Ax + By = C. Once the coefficients are integers and A is positive, rearrange the equation so it is in the form Ax + By = C. This means the x-term should come before the y-term and C should be on the opposite side of the equation as the variables.

Check your work. Once the equation is in standard form, check your work to ensure that it is correct.

Here’s an example of how to write an equation in standard form:

Given the equation 2x – 3y = 6, we can write it in standard form as follows:

2x – 3y = 6 (original equation)
2x – 3y + 3y = 6 + 3y (add 3y to both sides to move all variables to one side)
2x = 3y + 6 (simplify)
3y + 6 = 2x (rearrange the equation so it is in standard form) (rearrange the equation so it is in standard form)
2x – 3y = 6 (final equation in standard form)

In this example, the equation was simplified by moving all variables to one side of the equation and all constants to the other side. The coefficients were then converted to integers and A was made positive. Finally, the equation was rearranged so it was in the standard form Ax + By = C.

By following these guidelines, you can effectively write an equation in standard form. Simplify the equation, ensure the coefficients are integers, make sure A is positive, write the equation in the form Ax + By = C, and check your work to ensure that it is correct.