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WARM UP

Determine if lines are parallel or perpendicular, find slopes, compare slopes, and write equations of parallel and perpendicular lines.

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WARM UP

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  1. WARM UP

  2. Section 5 - 6Parallel & Perpendicular Lines Objectives: To determine whether lines are parallel, perpendicular or neither.

  3. Parallel Lines: Two lines in the same plane that do not intersect

  4. Perpendicular Lines: Two lines in the same plane that do not intersect

  5. Investigation For each coordinate plan: • Determine if the lines are parallel or perpendicular • Find the slope of each line • Compare the slopes Once you have found & compared the slopes of the lines on each coordinate plane, make a statement about the slopes of all parallel lines and all perpendicular lines.

  6. Slopes of Parallel Lines Nonvertical Lines have the same slope and different y-intercepts Vertical Lines have different x-intercepts *Lines that have the same slope AND the same y-intercept are THE SAME LINE!

  7. Example:

  8. Slopes of Perpendicular Lines Nonvertical Lines have slopes that have a product of -1 (they will be opposite reciprocals) A Vertical Line & A Horizontal Line are Perpendicular

  9. Example:

  10. Opposite Reciprocals

  11. Parallel? Perpendicular? Neither? , , , , y = 2, x = 8

  12. Problem # 2: Classifying Lines A) Are the graphs of 4y = -5x + 12 and parallel, perpendicular, or neither? Explain.

  13. Problem # 2: Classifying Lines B) Are the graphs of 4x – 3y = 9 and parallel, perpendicular, or neither? Explain.

  14. Problem #2Got It? Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain. 1) 2)

  15. HOMEWORK Textbook Page 334; #13 – 18 All

  16. WARM UP 1) How do you know if two lines are parallel? 2) How do you know if two lines are perpendicular?

  17. Section 5 - 6Parallel & Perpendicular Lines Objectives: To write equations of parallel and perpendicular lines

  18. Problem # 1: Writing an Equation of a Parallel Line A) A line passes through (12, 5) and is parallel to the graph of . What equation represents the line in slope-intercept form?

  19. Problem # 1: Writing an Equation of a Parallel Line B) A line passes through (-3, -1) and is parallel to the graph of . What equation represents the line in slope-intercept form?

  20. Problem #1Got It? What is an equation in slope-intercept form of the line that passes through (2, 15) and is parallel to the graph of y = 4x – 1?

  21. Problem # 3: Writing an Equation of a Perpendicular Line A) A line passes through (1, 8) and is perpendicular to the graph of y = 2x + 1. What equation represents the line in slope-intercept form?

  22. Problem # 3: Writing an Equation of a Perpendicular Line B) Which equation represents the line that passes through (2, 4) and is perpendicular to the graph of ?

  23. Problem #3Got It? The graph of which equation passes through (10, 15) and is perpendicular to the graph of ?

  24. HOMEWORK Textbook Page 334; #8 – 12 Even, 20 – 24 Even

  25. WARM UP Determine whether each statement is always, sometimes or never true. Explain. A horizontal line is parallel to the x=axis. Two lines with positive slopes are parallel. Two lines with the same slope and different y-intercepts are perpendicular.

  26. Section 5 - 6Parallel & Perpendicular Lines Objectives: To write equations of parallel and perpendicular lines

  27. Problem # 4: Solving a Real- World Problem A) An architect uses software to design the ceiling of a room. The architect needs to enter an equation that represents a new beam. The new beam will be perpendicular to the existing beam, which is represented by the red line. The new beam will pass through the corner represented by the blue point. What is an equation that represents the new beam?

  28. Problem # 4: Solving a Real- World Problem B) Carla is using a coordinate grid to make a map of her hometown. She plots Main Street as shown. If 3rd Street is perpendicular to Main Street at (5, 7), what is an equation for 3rd Street?

  29. Problem #4Got It? What is an equation in slope-intercept form of the line that passes through (6, -7) and is perpendicular to the line below?

  30. HOMEWORK 5 – 6 Standardized Test Prep Worksheet

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