Goal
Convert a line from slope-intercept form into standard form.
Main idea
Slope-intercept form looks like
[
y = mx + b
]
Standard form is usually written as
[
Ax + By = C
]
The task is to rewrite the same line so the variables are on the same side and the expression is simplified.
Method
- Start with the given equation in slope-intercept form.
- Move the x-term and/or constant term so that all variable terms are on one side.
- Often, this means adding or subtracting the same term from both sides.
- Arrange the equation into the form (Ax + By = C).
- Simplify coefficients and constants.
- If fractions appear, clear them if needed by multiplying every term by the common denominator.
- If all terms share a common factor, reduce the equation.
- Check the sign convention.
- Many standard-form answers keep the x-term positive if possible.
- If the first coefficient is negative, multiplying the entire equation by (-1) is often helpful.
Quick check
Substitute the same values into both forms, or verify that rearranging your final standard form returns the original slope-intercept equation.
Common mistake to avoid
Do not change only one side of the equation. Whatever operation you do, apply it to both sides equally.