Parallel and Perpendicular Lines

MGSE9-12.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Comparing slopes

What type of lines are these? Move your mouse over the image to review.

Slope Formula The slope, m, of a line passing through two arbitrary points (x1, y1) and (x2, y2) is calculated as follows…  CHANGE IN Y'S OVER CHANGE IN X'S

The slope, m, of a line passing through two arbitrary points (x1, y1) and (x2, y2) is calculated as follows… OVER

The negative reciprocal of the slope 5 is

  • -5
  • 1/5
  • -1/5

Practice

y = 3x + 5;     y = -1/3 x + 5

  • parallel
  • perpendicular
  • neither

y = 3x + 7; y = 7x + 3

  • parallel
  • perpendicular
  • neither

y = 2/3 x + 8; y = -3/2 x + 8

  • parallel
  • perpendicular
  • neither

Which slope would make these lines perpendicular?

  • -4/3

Slopes in equations

Which slope matches the equation?

  • y = 3x + 5
    y = 3x + 9; parallel
  • y = 3x + 5
    y = -1/3 x +7; perpendicular
  • y = 3x + 5
    y = -3x -5; neither