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Equations of Nonvertical Lines and Parallel/Perpendicular Lines - Lesson Summary

This summary provides key concepts and examples for writing equations of nonvertical lines and parallel/perpendicular lines. It covers slope-intercept form, point-slope form, and finding equations given slope and a point or two points. The summary also includes examples of writing equations for horizontal lines and real-world applications.

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Equations of Nonvertical Lines and Parallel/Perpendicular Lines - Lesson Summary

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 3–3) CCSS Then/Now New Vocabulary Key Concept: Nonvertical Line Equations Example 1: Slope and y-intercept Example 2: Slope and a Point on the Line Example 3: Two Points Example 4: Horizontal Line Key Concept: Horizontal and Vertical Line Equations Example 5: Write Equations of Parallel or Perpendicular Lines Example 6: Real-World Example: Write Linear Equations Lesson Menu

  3. What is the slope of the line MN for M(–3, 4) and N(5, –8)? A. B. C. D. 5-Minute Check 1

  4. What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)? A. B. C. D. 5-Minute Check 2

  5. What is the slope of a line parallel to MN forM(–3, 4) and N(5, –8)? A. B. C. D. 5-Minute Check 3

  6. A.B. C.D. What is the graph of the line that has slope 4 and contains the point (1, 2)? 5-Minute Check 4

  7. A. B. C. D. What is the graph of the line that has slope 0 and contains the point (–3, –4)? 5-Minute Check 5

  8. A.(–2, 2) B.(–1, 3) C.(3, 3) D.(4, 2) 5-Minute Check 6

  9. Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Mathematical Practices 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. CCSS

  10. You found the slopes of lines. • Write an equation of a line given information about the graph. • Solve problems by writing equations. Then/Now

  11. slope-intercept form • point-slope form Vocabulary

  12. Concept

  13. Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line. Slope and y-intercept y = mx + b Slope-intercept form y = 6x + (–3) m = 6, b = –3 y = 6x – 3 Simplify. Example 1

  14. Use the slope of 6 or to findanother point 6 units up and1 unit right of the y-intercept. Slope and y-intercept Answer: Plot a point at the y-intercept, –3. Draw a line through these two points. Example 1

  15. Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4. A.x + y = 4 B.y = x – 4 C.y = –x – 4 D.y = –x + 4 Example 1

  16. Write an equation in point-slope form of the linewhose slope is that contains (–10, 8). Then graph the line. Slope and a Point on the Line Point-slope form Simplify. Example 2

  17. Use the slopeto find another point 3 units down and 5 units to the right. Slope and a Point on the Line Answer: Graph the given point (–10, 8). Draw a line through these two points. Example 2

  18. Write an equation in point-slope form of the linewhose slope is that contains (6, –3). A. B. C. D. Example 2

  19. A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0). Two Points Step 1 First, find the slope of the line. Slope formula x1 = 4, x2 = –2, y1 = 9, y2 = 0 Simplify. Example 3

  20. Using (4, 9): Point-slope form Answer: Two Points Step 2 Now use the point-slope form and either point to write an equation. Distributive Property Add 9 to each side. Example 3

  21. B.Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3). Two Points Step 1 First, find the slope of the line. Slope formula x1 = –3, x2 = –1, y1 = –7, y2 = 3 Simplify. Example 3

  22. Using (–1, 3): Point-slope form y = 5x + 8 Add 3 to each side. Answer: Two Points Step 2 Now use the point-slope form and either point to write an equation. m = 5, (x1, y1) = (–1, 3) Distributive Property Example 3

  23. A. B. C. D. A. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8). Example 3a

  24. B. Write an equation in slope-intercept form for a line containing (1, 1) and (4, 10). A.y = 2x – 3 B.y = 2x + 1 C.y = 3x – 2 D.y = 3x + 1 Example 3b

  25. Horizontal Line Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form. Step 1 Slope formula This is a horizontal line. Example 4

  26. Answer: y = –2 Subtract 2 from each side. Horizontal Line Step 2 Point-Slope form m = 0, (x1, y1) = (5, –2) Simplify. Example 4

  27. A. B. C. D. Write an equation of the line through (–3, 6) and (9, –2) in slope-intercept form. Example 4

  28. Concept

  29. Write Equations of Parallel or Perpendicular Lines y = mx + b Slope-Intercept form 0 = –5(2) + bm = –5, (x, y) = (2, 0) 0 = –10 + b Simplify. 10 = b Add 10 to each side. Answer:So, the equation is y = –5x + 10. Example 5

  30. A.y = 3x B.y = 3x + 8 C.y = –3x + 8 D. Example 5

  31. Write Linear Equations RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. A. Write an equation to represent the total first year’s cost A for r months of rent. For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750. A= mr+b Slope-intercept form A= 525r + 750 m = 525, b = 750 Answer: The total annual cost can be represented by the equation A = 525r + 750. Example 6

  32. Write Linear Equations RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. B. Compare this rental cost to a complex which charges a $200 annual maintenance fee but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate? Evaluate each equation for r = 12. First complex:Second complex: A= 525r + 750 A = 600r + 200 = 525(12) + 750 r = 12 = 600(12) + 200 = 7050 Simplify. = 7400 Example 6

  33. Write Linear Equations Answer: The first complex offers the better rate: one year costs $7050 instead of $7400. Example 6

  34. RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. A. Write an equation to represent the total cost C for d days of use. A.C = 25 + d + 100 B.C = 125d C.C = 100d + 25 D.C = 25d + 100 Example 6a

  35. RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. B. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate? A. first company B. second company C. neither D. cannot be determined Example 6b

  36. End of the Lesson

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