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Precalculus Warm-up: 1/26/2012

This precalculus warm-up includes solving equations for parallel and perpendicular lines, linear modeling for word problems, and understanding slope as a ratio or rate. Real-life applications such as wheelchair ramp slope and sales prediction are discussed. Detailed examples guide you through applying these concepts in different scenarios. Practice problems and quiz review questions with answers enhance learning. Explore how slope determines line relationships and analyze the slope-intercept form for predictions. Master the concepts to identify parallel, perpendicular, or neither lines effectively in geometry.

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Precalculus Warm-up: 1/26/2012

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  1. Precalculus Warm-up: 1/26/2012

  2. Answers

  3. Check Homework • Quiz Review p. 9 #51, 53 p. 21 #13, 48, 59, 71, 73, 75, 79, 81 Take Quiz 1.1-1.2

  4. Lesson 1.3(b) Objective: 1-Write an equation of a line parallel and perpendicular to a given line. 2-Write a linear model to represent word problems.

  5. Parallel and Perpendicular Lines • Slope can be used to decide whether two non-vertical lines in a plane are parallel, perpendicular, or neither.

  6. Find all forms of the equation of the line that; • passes through the point (-4, 1) and is parallel to 5x – 3y = 8. • passes through the point (-4, 1) and is perpendicular to 5x – 3y = 8.

  7. Applications • In real-life problems, the slope of a line can be interpreted as either a ratio or a rate. • If the x-axis and y-axis have the same unit of measure, then the slope has no units and is a ratio. • If the x-axis and y-axis have different units of measure, then the slope is a rate or rate of change.

  8. Example 5 – Using Slope as a Ratio The maximum recommended slope of a wheelchair ramp is A business is installing a wheelchair ramp that rises 22 inches over a horizontal length of 24 feet. Is the ramp steeper than recommended? (Source: Americans with Disabilities Act Handbook)

  9. Example 5 – Solution • The horizontal length of the ramp is 24 feet or12(24) = 288 inches, as shown in Figure 1.41. Figure 1.41

  10. Example 5 – Solution cont’d So, the slope of the ramp is Because  0.083, the slope of the ramp is not steeper than recommended.

  11. Example 8 – Predicting Sales The sales for Best Buy were approximately $35.9 billion in 2006 and $40.0 billion in 2007. Using only this information, write a linear equation that gives the sales (in billions of dollars) in terms of the year. Then predict the sales for 2010. (Source: Best Buy Company, Inc.)

  12. Example 8 – Solution Let t = 6 represent 2006. Then the two given values are represented by the data points (6, 35.9) and (7, 40.0). The slope of the line through these points is 4.1 Using the point-slope form, you can find the equation that relates the sales y and the year t to be y – 35.9 = 4.1(t – 6)

  13. Write in slope-intercept form. Example 8 – Solution cont’d y = 4.1t + 11.3. According to this equation, the sales for 2010 will be y = 4.1(10)+ 11.3 = 41+ 11.3 = $52.3 billion. (Figure 1.44.) Figure 1.44

  14. Finish “notes 1.3” • Summary on page 32

  15. Homework P. 33 # 24, 38, 48, 60, 70, 82, 88, 90, 126, 130 Closure: Determine if the lines are parallel, perpendicular, or neither. Answers Parallel Perpendicular

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