Key Concepts in Linear Equations and Slope

Slope-Intercept Form

• Equation of a line expressed as: $y = mx + b$
• $m$ = slope, $b$ = y-intercept.

Finding the Equation of the Line

• Use given point (example: (5,2)) and slope (example: -1/3).
• Point-slope form: $y - y<em>1 = m(x - x</em>1)$
• Substitute values and simplify.

Steps to Solve

1. Identify $x1, y1$ from the point, and slope $m$.
2. Write the equation in point-slope form.
3. Rearrange to slope-intercept form: $y = mx + b$.

Standard Form of a Line

• Standard form as: $Ax + By = C$, where A, B, C are integers and $A$ is non-negative.

Converting to Standard Form

1. Rearrange terms to get $Ax + By = C$.
2. If fractions are present, multiply through by a common denominator to eliminate them.
3. Ensure coefficients are integers and $A$ is positive.

Important Notes

• Remember that both slope-intercept and standard form are commonly used.
• Pay attention to positive coefficients in standard form for accuracy on tests.