Converting Slope-Intercept to Standard Form
Converting a linear equation from slope-intercept form y = mx + b to standard form Ax + By = C requires moving all variable terms to the left side and the constant to the right, with A, B, C as integers sharing no common factors — a key skill in enVision Algebra 1 Chapter 2 for Grade 11. For y = 3x + 5, subtract 3x from both sides to get -3x + y = 5, or equivalently 3x - y = -5. For fractional slopes like y = -⅔x + 4, first multiply through by 3 to clear fractions (3y = -2x + 12), then rearrange to 2x + 3y = 12.
Key Concepts
To convert from slope intercept form $y = mx + b$ to standard form $Ax + By = C$, rearrange the equation so that all variable terms are on the left side and the constant is on the right side. Ensure that $A$, $B$, and $C$ are integers with no common factors.
Common Questions
How do you convert y = 3x + 5 to standard form?
Move 3x to the left side: -3x + y = 5. To make A positive, multiply through by -1: 3x - y = -5.
How do you handle fractional slopes when converting to standard form?
Multiply the entire equation by the denominator to clear fractions first. For y = -⅔x + 4, multiply by 3: 3y = -2x + 12, then rearrange: 2x + 3y = 12.
How do you convert y = -x - 7 to standard form?
Add x to both sides: x + y = -7. This is already in standard form with A = 1, B = 1, C = -7.
What requirements must A, B, C satisfy in standard form?
A, B, and C must be integers with no common factors, and conventionally A ≥ 0. If A is negative, multiply the whole equation by -1.
Why is standard form useful compared to slope-intercept form?
Standard form makes it easy to find both intercepts by substitution (set x=0 or y=0). It also works well for the elimination method when solving systems of equations.