Summary: Writing Equations of Lines

Key Concepts

Graph a line given a point and a slope

  1. Plot the given point.
  2. Use the slope formula to identify the rise and the run.
  3. Starting at the given point, count out the rise and run to mark the second point.
  4. Connect the points with a line.

Slope-Intercept Form of a Linear Equation

In the equation [latex]y=mx+b[/latex],

  • m is the slope of the graph.
  • b is the y value of the y-intercept of the graph.

Parallel Lines

Two non-vertical lines in a plane are parallel if they have both:

  • the same slope
  • different [latex]y[/latex]-intercepts

Any two vertical lines in a plane are parallel.

Perpendicular Lines  Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. If the slope of one line is m, then the slope of the perpendicular line is [latex]\frac{-1}{m}[/latex].