Converting Linear Equations to Standard Form: A Guide

Standard Form

Standard form, also known as standard equation form or general form, is a way of writing linear equations

Standard form, also known as standard equation form or general form, is a way of writing linear equations.

In general, a linear equation can be written in the form: Ax + By = C, where A, B, and C are constants, and A and B are not both zero. This form is called the standard form.

Here’s a breakdown of the variables in the standard form equation:

– x and y represent the variables in the equation. These are the unknown values that we are trying to solve for.
– A, B, and C are constants. A and B are the coefficients of x and y, respectively, while C is a constant term.

To convert a linear equation from slope-intercept form (y = mx + b) or point-slope form (y – y1 = m(x – x1)) to standard form, we follow these steps:

1. Simplify the equation so that the variables (x and y) are on one side and the constant on the other.
2. Arrange the equation so that the x and y terms are on the left side, and the constant term is on the right side.
3. Multiply through the equation by a common multiple of the coefficients to clear any fractions or decimals, if necessary.
4. Rearrange the equation, if needed, so that the coefficients A and B are integers, and A is positive.

Let’s look at an example:

Convert the equation y = 2x + 3 to standard form.

Step 1: Simplify the equation.
y = 2x + 3

Step 2: Arrange the equation.
2x – y = -3

Step 3: Multiply through the equation.
2(2x) – 2(y) = 2(-3)
4x – 2y = -6

Step 4: Rearrange the equation.
4x – 2y + 6 = 0

Therefore, the standard form of the equation y = 2x + 3 is 4x – 2y + 6 = 0.

It’s worth noting that in the standard form, A is always non-negative (positive or zero), and if A is zero, then B must be non-zero. The equation can also be adjusted so that A, B, and C are integers and their greatest common divisor is 1.

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