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Unit 5: Analytic Geometry

Unit 5: Analytic Geometry. Minds On. Determine the equation of this line:. Unit 5: Analytic Geometry. Lesson 7 – Special Cases. Determine the equation of your graph. Compare how your graph looks with how your partner’s graph looks Compare your equations. Unit 5: Analytic Geometry.

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Unit 5: Analytic Geometry

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  1. Unit 5: Analytic Geometry Minds On Determine the equation of this line:

  2. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Determine the equation of your graph. • Compare how your graph looks with how your partner’s graph looks • Compare your equations

  3. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Compare your Graphs

  4. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Compare your equations

  5. Unit 5: Analytic Geometry Lesson 7 – Special Cases What can we conclude?

  6. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Do you think this is always true? Why or why not? • Lets find out! With your partner come up with 2 sets of equations with equal slopes and then we will graph them. Are they parallel?

  7. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Determine the equation of your graph. • Compare how your graph looks with how your partner’s graph looks • Compare your equations

  8. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Compare your graphs

  9. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Compare your equations

  10. Unit 5: Analytic Geometry Lesson 7 – Special Cases What can we conclude?

  11. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Do you think this is always true? Why or why not? • Lets find out! With your partner come up with 2 sets of equations with slopes that are negative reciprocals and we will graph them. Are they perpendicular?

  12. Unit 5: Analytic Geometry Lesson 7 – Special Cases • A line is parallel to the line y = 3x -7. What could the equation of the line be? • How do you know? • Are there other possibilities? • Could the line go downward to the right?

  13. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Two lines are perpendicular. One has a y-intercept of 4 and the other has a y-intercept of -3. What could the equations be? • How do you know? • Can both lines have positive slopes? • Can both lines have negative slopes? • Can either line have the positive slope?

  14. Unit 5: Analytic Geometry Lesson 7 – Special Cases Let’s determine the slopes of these lines: Do you see a pattern?

  15. Unit 5: Analytic Geometry Lesson 7 – Special Cases • What do you think the slope of this line is? • Discuss with your partner. • Think about how you would calculate it:

  16. Unit 5: Analytic Geometry Lesson 7 – Special Cases Horizontal lines have a slope of zero. m = 0

  17. Unit 5: Analytic Geometry Lesson 7 – Special Cases Let’s determine the slope of these lines: Do you see a pattern?

  18. Unit 5: Analytic Geometry Lesson 7 – Special Cases • What do you think the slope of this line is? • Discuss with your partner. • Think about how you would calculate it:

  19. Unit 5: Analytic Geometry Lesson 7 – Special Cases Vertical lines have a slope that is undefined. m =

  20. Unit 5: Analytic Geometry Lesson 7 – Special Cases • Remember, the y-intercept is represented by b. • And slope is represented by m. • The equation of a line is • y = mx + b

  21. Unit 5: Analytic Geometry Lesson 7 – Special Cases Determine the equation of this line:

  22. Unit 5: Analytic Geometry Lesson 7 – Special Cases What about horizontal and vertical lines?

  23. Unit 5: Analytic Geometry Lesson 7 – Special Cases Determine the equation of this line:

  24. Unit 5: Analytic Geometry Lesson 7 – Special Cases Determine the equation of this line:

  25. Unit 5: Analytic Geometry Lesson 7 – Special Cases Find the equation of a line that is parallel to the line y = 2x – 4 and passes through the point (4, 1).

  26. Unit 5: Analytic Geometry Lesson 7 – Special Cases Determine the equation of a line with a slope of 0 and a y-intercept of 4.

  27. Unit 5: Analytic Geometry Lesson 7 – Special Cases Find the equation of a line that is perpendicular to the line y = -3x + 6 and passes through the point (-2, 5).

  28. Unit 5: Analytic Geometry Lesson 7 – Special Cases Find the equation of a line that does not have a y-intercept, but has an x-intercept of 7.

  29. Unit 5: Analytic Geometry Lesson 7 – Special Cases Practice • Pg. 140 #2-10, 12, 13, 15

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