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Finding Equations of Parallel and Perpendicular Lines
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Homework
  • Improving Individual Responses to the Assessment Task (10 minutes)
      • Return students' original assessment tasks, along with a second, blank copy of the task sheet.
        • Look at your original responses, and think about what you have learned in this lesson.
        • Using what you have learned, try to improve your work.
      • If students are satisfied with their solutions, ask them to write down a general method for finding the equations of lines that form a rectangle.
  • Solutions: Parallel and Perpendicular Lines
    • Question 1.

      Students may first put the equation into the form y = mx + b and look for m, the slope.

      y + 2x = 8

      y = −2x + 8

      Slope = −2

      2y + ½x + 1 = 0

      y = −¼x − ½

      Slope = −¼

      2y + x = 1

      y = −½x + ½

      Slope = −½

      y = x − 4

      Slope = 1

      y = 2(x − 1)

      y = 2x − 2

      Slope = 2

      2y = x − 4

      y = ½x − 2

      Slope = ½

      y + 2x + 2 = 0

      y = −2x − 2

      Slope = −2

      y = ½x + 2

      Slope = ½

      y = 4 − x

      y = −x + 4

      Slope = −1

      2y = 4 − x

      y = −½x + 2

      Slope = −½

      The slopes of parallel lines are equal.

      The product of the slope of a line and its perpendicular is −1.

      These pairs of lines are parallel:

      y + 2x = 8 and y + 2x + 2 = 0

      2y = x − 4 and y = ½x + 2

      2y + x = 1 and 2y = 4 − x

      Lines y + 2x = 8 and y + 2x + 2 = 0 are perpendicular to 2y = x − 4 and y = ½x + 2, so these form a rectangle.

      Question 2.

      Lines y + 2x = 8 and y + 2x + 2 = 0 have a negative slope, so they are the parallel pair shown on the diagram.

      Lines 2y = x − 4 and y = ½x + 2 have a positive slope, so either 2y = x − 4 or y = ½x + 2 is the line that is missing.

      The y intercepts of lines 2y = 4 − x and y + 2x + 2 = 0 are the same, so these lines cross and intercept the y-axis at the point (0, −2).

      Line y = ½x + 2 can be positioned by finding the line that is parallel to 2y = x − 4 that passes through (0, 2) (y-intercept).

  • Solutions: Equations and Properties Task
    • These lines are parallel

      2y = 8x + 3

      y = 4x + 4

      These lines are perpendicular

      4y = x + 3

      y + 4x +6 = 0

      These lines have the same y-intercept

      y = 6x − 4

      2y + 8 = 3x

      These lines have the same x-intercept

      3y = 2x − 8

      2y + x = 4

      These lines go through the point (1,5)

      y + 6x = 11

      y = 8x − 3


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