Converting Linear Equations | From Slope-Intercept and Point-Slope to Standard Form

standard form of a linear equation

The standard form of a linear equation is a way to represent a linear equation in a standardized format

The standard form of a linear equation is a way to represent a linear equation in a standardized format. It is commonly written as:

Ax + By = C

In this form, A, B, and C are constants, and x and y are variables. A and B cannot both be zero simultaneously.

The standard form has several benefits when compared to other forms, such as slope-intercept form or point-slope form. One advantage is that it allows for easy comparison and manipulation of equations. For example, you can add or subtract multiple equations using the standard form to solve systems of equations. It also facilitates the identification of the x-intercept and y-intercept of the line represented by the equation.

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

1. For the slope-intercept form, rearrange the equation to isolate y on one side. This will give you an equation in the form y = mx + b.
2. Subtract mx from both sides to get -mx + y = b.
3. Rearrange the equation to match the standard form by rearranging the terms: -mx + y = b becomes -mx + y – b = 0.
4. Multiply the equation by -1 to make the coefficient of x positive: mx – y + b = 0.
5. Finally, if necessary, rearrange the equation so that the coefficients are integers and the equation is in the standard form: -y + mx = -b.

Converting an equation from point-slope form to standard form follows similar steps.

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