How to convert from slope intercept to standard form?
Understand the Problem
The question is asking for the method to convert an equation expressed in slope-intercept form (y = mx + b) into standard form (Ax + By = C). This involves rearranging the terms and potentially changing their coefficients to meet the standard form requirements.
Answer
mx - y = -b
Answer for screen readers
The final standard form of the equation is mx - y = -b
Steps to Solve
- Start with the slope-intercept form equation
Begin with the equation in the form $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.
- Rearrange terms to isolate the $x$ and $y$ terms on one side
Subtract $mx$ from both sides of the equation to move the $x$ term to the left side. This gives: $$ y - mx = b $$
- Rearrange to the standard form structure
Standard form requires the $x$ and $y$ terms on one side and the constant term on the other side. The equation will look like $$ -mx + y = b $$
- Multiply through by -1 if necessary
If the coefficient of $x$ is negative, multiply both sides by -1 to make it positive, resulting in: $$ mx - y = -b $$
The final standard form of the equation is mx - y = -b
More Information
The standard form, Ax + By = C, is useful for various applications such as linear programming and when analyzing intersections of lines.
Tips
A common mistake is forgetting to change the signs when necessary. Always check to ensure that all coefficients in your standard form are integers.
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