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Lesson 6.1b Writing Equations of Parallel and Perpendicular Lines

Lesson 6.1b Writing Equations of Parallel and Perpendicular Lines. Concept: writing equations of lines EQ: How do we write the equation of a line that is parallel or perpendicular to a given line? (G.GPE.5) Vocabulary : Slope, Parallel, perpendicular,

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Lesson 6.1b Writing Equations of Parallel and Perpendicular Lines

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  1. Lesson 6.1bWriting Equations of Parallel and Perpendicular Lines Concept: writing equations of lines EQ: How do we write the equation of a line that is parallel or perpendicular to a given line? (G.GPE.5) Vocabulary: Slope, Parallel, perpendicular, Reciprocal

  2. First word • Create an acrostic about everything you remember from the previous lesson using the word. • SLOPE

  3. Introduction • Parallel lines are lines which nevertouchor intersect. • Perpendicular lines are lines which meet or intersect and create a 90°angle aka a right angle. • We can find the equation of two lines which are parallel or perpendicular and prove whether the lines are parallel or perpendicular.

  4. Parallel Lines • Lines which are parallel always have the sameslope or value for m, but a different y-intercept or value for b. • Ex. are parallel lines because they have the same slope but different y-intercepts.

  5. Example 1 • Two lines, are linear equation. Line has the equation . Line has the equation. Are they parallel?

  6. Example 2 • The two lines in the graph to the right, are shown. Are they parallel?

  7. You try 1 • You are the given two equations of two different lines, Are these lines parallel?

  8. You try 2 • Are these lines parallel? Explain

  9. Example 3 • A line which contains the point (2,5) is parallel to the line . Find the equation to this line.

  10. Example 4 • Using the graph to the right, find the equation of a parallel line which passes through the point which is not on the given line.

  11. You try 3 • A line which contains the point (0,-11) is parallel to the line . Find the equation to this line.

  12. Perpendicular lines • Lines are always perpendicular if their slopes are a negativereciprocal of one another. Perpendicular lines can have the same y-intercepts though. • Ex. are perpendicular lines with the same y-intercepts. Another example would be . These two lines are perpendicular because of their slopes but have different y-intercepts.

  13. Example 5 • Two lines are given,. Are they perpendicular?

  14. Example 6 • The two lines in the graph to the right, are shown. We need to determine if the two lines are perpendicular.

  15. You try 4 • You are given two equations, Are these two lines perpendicular?

  16. You try 5 • Are these lines perpendicular? Explain

  17. Example 7 • A line which contains the point (2,5) is perpendicular to the line . Find the equation to this line.

  18. Example 8 • Using the graph to the right, find the equation of a parallel line which passes through the point which is not on the given line.

  19. You try 6 • A line which contains the point (0,5) is perpendicular to the line . Find the equation to this line.

  20. 3-2-1 • List three important facts you learned about today. • List two concepts you already knew. • List one task you still need to work on.

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