Key Concepts

Key Concepts

• To Find an Equation of a Line Given the Slope and a Point
  
  1. Identify the slope.
  2. Identify the point.
  3. Substitute the values into the point-slope form, \(y-{y}_{1}=m\left(x-{x}_{1}\right)\).
  4. Write the equation in slope-intercept form.
• To Find an Equation of a Line Given Two Points
  
  1. Find the slope using the given points.
  2. Choose one point.
  3. Substitute the values into the point-slope form, \(y-{y}_{1}=m\left(x-{x}_{1}\right)\).
  4. Write the equation in slope-intercept form.
• To Write and Equation of a Line
  
  • If given slope and y-intercept, use slope–intercept form \(y=mx+b\).
  • If given slope and a point, use point–slope form \(y-{y}_{1}=m\left(x-{x}_{1}\right)\).
  • If given two points, use point–slope form \(y-{y}_{1}=m\left(x-{x}_{1}\right)\).
• To Find an Equation of a Line Parallel to a Given Line
  
  1. Find the slope of the given line.
  2. Find the slope of the parallel line.
  3. Identify the point.
  4. Substitute the values into the point-slope form, \(y-{y}_{1}=m\left(x-{x}_{1}\right)\).
  5. Write the equation in slope-intercept form.
• To Find an Equation of a Line Perpendicular to a Given Line
  
  1. Find the slope of the given line.
  2. Find the slope of the perpendicular line.
  3. Identify the point.
  4. Substitute the values into the point-slope form, \(y-{y}_{1}=m\left(x-{x}_{1}\right)\).
  5. Write the equation in slope-intercept form.

Glossary

point–slope form

The point–slope form of an equation of a line with slope $m$ and containing the point $(x_1,y_1)$ is $y−y_1=m(x−x_1)$.