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Lesson 5.5

Lesson 5.5. Parallel and Perpendicular Lines. Alg 7.0 Derive linear equations by using the point-slope formula. Alg 8.0

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Lesson 5.5

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  1. Lesson 5.5 Parallel and Perpendicular Lines

  2. Alg 7.0 Derive linear equations by using the point-slope formula. Alg 8.0 Understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Find the equation of a line perpendicular to a given line that passes through a given point.

  3. Lesson Objective: Students will be able to write equations of parallel and perpendicular lines as demonstrated by a Ticket out the Door.

  4. Graph the following on the coordinate plane. y x Parallel lines have the same slope.

  5. Think Pair Share: Parallel lines Two lines are parallel if they never intersect. Example: Parallel lines Not parallel lines What do we know about the slope of parallel lines?

  6. Graph the following on the coordinate plane. y x Lines appear perpendicular Perpendicular lines have slopes that are opposite reciprocals

  7. Perpendicular Lines Two lines are perpendicular if they intersect to form right angles. Example: Not perpendicular Perpendicular What do we know about the slope of perpendicular lines? Think Pair Share: Lines are perpendicular if the product of the slopes is -1 (opposite andreciprocal).

  8. Example 1: m=2 I Do! Find the slopeonly of a line paralleland perpendicular to the graph of each equation. Example 2:

  9. We Do! Find the slope of a line parallel and perpendicular to the graph of each equation.

  10. Think Pair Share: We Do! Find the slope of a line parallel and perpendicular to the graph of each equation.

  11. Partner A on the White Board You Do! Find the slope of a line parallel and perpendicular to the graph of each equation. Partner B on the White Board

  12. Determine if the lines in each pair are parallel or perpendicular?

  13. Part 1: Parallel Lines

  14. Parallel lines: Lines are parallel if they have the same slope but different y-intercepts.

  15. Write in slope-intercept form the equation of the line that is parallel to the line in the graph and passes through the given point.

  16. Flow map for parallel lines: Step 1: Determinethe slope that you will need m = Point-Slope Form • Step 2:take the given point • x1 = • y1 = • Step 3:plug the point and slope into the point - slope formula • y – y1 = m(x – x1) • Step 4:distribute and solve for “y” • y = mx + b Slope-Intercept Form Stop here if the question asks for Point Slope Form

  17. I Do! Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (6, 2).

  18. We Do! Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (-4, -6).

  19. You Do! Partner A on the Whiteboard: Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (0,1).

  20. You Do! Partner B on the Whiteboard: Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (-3,5).

  21. Part 2: Perpendicular Lines

  22. Perpendicular lines Lines are perpendicular if the product of their slopes equals −1 The slopes are: *opposite *reciprocal

  23. Write in slope-intercept form the equation of the line that is perpendicularto the line in the graph and passes through the given point.

  24. I Do! Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (6, 2).

  25. We Do! Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (0, 1).

  26. You Do! Partner A on the Whiteboard Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (-1, 2).

  27. You Do! Partner B on the Whiteboard Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (-1, -2).

  28. Summary • Parallel Lines: They have the same exact slope (m) and different y-intercepts (b) • Perpendicular Lines: Their slopes are opposite (change the sign) and reciprocals (flip)of each other.

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