- Slides: 12
Lesson 5. 2. 2 – Teacher Notes Standard: 8. EE. C. 8 c Analyze and solve pairs of simultaneous linear equations. c) Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. • Full mastery can be expected by the end of the chapter. Lesson Focus: The focus of this lesson is to give students additional practice with both real-world and mathematical tasks. (5 -32 and 5 -35) • I can solve mathematical problems leading to two linear equations in two variables. Calculator: Yes Literacy/Teaching Strategy: Teammates Consult and/or Huddle (5 -32); Silent Debate(5 -35); Give One Get One and Whip Around (Closure)
In Lesson 5. 2. 1, you discovered that the point of intersection of two lines or curves can have an important meaning. Finding points of intersection is another strategy you can use to solve problems, especially those with two quantities being compared. Analyze the following situations using the multiple tools you have studied so far.
5 -32. BUYING BICYCLES Latanya and George are saving up money because they both want to buy new bicycles. Latanya opened a savings account with $50. She just got a job and is determined to save an additional $30 a week. George started a savings account with $75. He is able to save $25 a week.
Your Task: Use at least two different ways to find the time (in weeks) when Latanya and George will have the same amount of money in their savings accounts. Be prepared to share your methods with the class.
5 -35. Gerardo decided to use tables to find the point of intersection of the lines y = 4 x − 6 and y = − 2 x + 3. His tables are shown below. Y = 4 x -6 Y= -2 x + 3
5 -35. Continued a. Examine his tables. Is there a common point that makes both rules true? If not, can you describe where the point of intersection is? b. Now graph the rules on the same set of axes. Where do the lines intersect? c. Use the rules to confirm your answer to part (b). Y = 4 x -6 Y= -2 x + 3
Extra Practice 1. Your cell phone plan costs 15 dollars a month, plus 10 cents per minute. Write an equation to model the money you will spend each month on your cell phone.
Extra Practice 2. Jacques will wash the windows of a house for $15. 00 plus $1. 00 per window. Ray will wash them for $5. 00 plus $2. 00 per window. Let x be the number of windows and y be the total charge for washing them. Write an equation that represents how much each person charges to wash windows. x
Extra Practice 3. Elle has moved to Hawksbluff for one year and wants to join a health club. She has narrowed her choices to two places: Thigh Hopes and ABSolutely f. ABulus. Thigh Hopes charges a fee of $95 to join and an additional $15 per month. ABSolutely f. ABulus charges a fee of $125 to join and a monthly fee of $12. Write two equations that represent each club's charges. x
Extra Practice 4. Nancy started the year with $425 in the bank and is saving $25 a week. Seamus started with $875 and is spending $15 a week. Write two equations that represent Nancy and Seamus’s bank account.
Extra Practice 5. Larry and his sister, Betty, are saving money to buy their own laptop computers. Larry has $215 and can save $35 each week. Betty has $380 and can save $20 each week. Write two equations that represent Larry and Betty’s savings.