1. Algebra-2 Word Problems (linear equations)

2. Quiz 1. Which ordered pair is a solution of: a. (-1, 1) b. (2, -1) c. (1, 2) 2. Yes/no: is the point a solution of the inequality? (1, 1) (1, 1) 3. Graph the following inequality.

3. Quiz 1. Find the slope intercept form of a line that passes through the point (4, 5) and is perpendicular to the line: y = -1/3 x – 2 2. Solve for x: 3. Solve the inequality. 18 + 2x ≥ 9x + 4 4. Graph the inequality of problem #3 above.

4. Linear Word Problems

5. Slope time distance What are the “units” of the x-axis? What are the “units” of the y-axis? Slope =

6. Slope Slope is a ratio. ‘Mph’ (speed) means what?

7. Slope y x weight Price= What are the “units” of the x-axis? What are the “units” of the y-axis?

8. Slope Slope is a ratio. ‘Dollars per pound mean? “the ‘price’ for each “unit of weight”.

9. Slope y x = What are the “units” of the x-axis? What are the “units” of the y-axis? 1 person 0.5 candy bars 40 people 20 candy bars

10. Slope Slope is a ratio. ‘candy bars per person “the number of candy bars each person gets.

11. Your turn: Find the “rate”  ratio change of one quantity to the change in another quantity for the following in another quantity for the following include the units!!! include the units!!! 1. The level in the tank changed from 20 gallons to 40 gallons over a 5 minute period. over a 5 minute period. 2. The number of people in the stadium changed from 200 people to 100 people during a 2 minute period. 200 people to 100 people during a 2 minute period. 3. The temperature of the solution changed from 75° F. to 100° F during a 10 minute period. 75° F. to 100° F during a 10 minute period.

12. Your turn: Identify the input and output variables for each include units!!! 4. The level in the tank changed from 20 gallons to 40 gallons over a 5 minute period. over a 5 minute period. 5. The number of people in the stadium changed from 200 people to 100 people during a 2 minute period. 200 people to 100 people during a 2 minute period. 6. The temperature of the solution changed from 75° F. to 100° F during a 10 minute period. 75° F. to 100° F during a 10 minute period.

13. Word Problems modeled by a line: A fixed amount PLUS an amount based upon the number of items used/bought/etc. items used/bought/etc. Example #1: The cost of membership to the club is $50 plus $5 per visit. $5 per visit. (1) Write the equation for this relation (1) Write the equation for this relation (2) What would be the membership cost for 40 visits? (2) What would be the membership cost for 40 visits? What is the slope? What is the slope? What is the input variable? What is the input variable? What is the output when the input is zero? What is the output when the input is zero?

14. Word Problems modeled by a line: A fixed amount PLUS an amount based upon the number of items used/bought/etc. items used/bought/etc. Example #1: The cost of membership to the club is $50 plus $5 per visit. per visit. (1) Write the equation for this relation. b = $50 (2) What would be the membership cost for 40 visits?

15. Word Problems modeled by a line: A fixed amount PLUS an amount based upon the number of items used/bought/etc. items used/bought/etc. Example #2: A cell phone company charges $30 plus $0.03 per minute of usage. (1)Write the equation for this relation. (2) What will it cost this month if you used 500 minutes? What is the slope? What is the slope? What is the input variable? What is the input variable? What is the output when the input is zero? What is the output when the input is zero?

16. Word Problems modeled by a line: A fixed amount PLUS an amount based upon the number of items used/bought/etc. items used/bought/etc. b = $30 Example #2: A cell phone company charges $30 plus $0.03 per minute of usage. (1)Write the equation for this relation. (2) What will it cost this month if you used 500 minutes?

17. Your Turn: 7. A membership to a health club costs $25 plus $1 per visit. a.Write an equation to represent the cost of membership. b.How much would the membership cost if you visited 30 times? 8. A monthly cell phone plan costs $10 plus 0.02 per minute. a.Write an equation to represent the cost of the phone. b.How much would the phone cost if you used it 120 minutes?

18. A little “wrinkle” What happens if the cost per usage doesn’t come into effect until after a certain amount of usage? To lease a Rolls Royce for a year, you must pay $25000 plus $0.50 per mile you drive over 5,000 miles. You drive the car 11,000 miles. What is the cost of the car for the year? the car 11,000 miles. What is the cost of the car for the year? Subtract 5000 miles from the # of miles driven

19. A little “wrinkle” To lease a Rolls Royce for a year, you must pay $25000 plus $0.50 for every mile you drive over 5,000 miles. You drive the car 11,000 miles. What is the cost of the car for the year? the car 11,000 miles. What is the cost of the car for the year? Subtract 5000 miles from the # of miles driven

20. Your Turn: To lease a Honda Accord for a year, you must pay $3000 plus $0.20 for every mile you drive over 10,000 miles. You drive the car 12,000 miles. the car 12,000 miles. 9. Write an equation for this relation. 10. What is the cost of the car for the year? To lease a Mercedes 280i for a year, you must pay $5000 plus $0.30 for every mile you drive over 8,000 miles. You drive the car 11,000 miles. the car 11,000 miles. 11. Write an equation for this relation. 12. What is the cost of the car for the year?

21. Standard Form Linear word problems These type usually are total cost of two items. Pizzas cost $5 each. Drinks cost $1.25 each. 1. Write an equation that shows the total cost of buying pizzas and drinks. 2. What is the total cost if you buy 10 pizzas and 30 drinks?

22. Standard Form Equations Nails cost $5 per pound. Screws cost $10 per pound. Write an equation showing how many pounds of nails and screws you can buy if you can spend $30. you can buy if you can spend $30. # lbs of screws bought 5n + 10s = 30 # lbs nails (or #lbs screws) 1. Decide upon the units of the x-axis. 2. Decide upon the units of the y-axis. The cost of any combination of nails and screws must equal to $30

23. Your Turn: Large soda fountain drinks cost $2.50. Small drinks cost $1.50. Your budget for the party is $25 13. Write an equation for this relation. 14. If you buy 7 large drinks, how many small drinks can you buy?

24. Your turn. Small pizzas cost $7 each. Large pizzas cost $10 each. Write an equation showing relating the number of large and small pizzas that can be bought if you can spend $50. pizzas that can be bought if you can spend $50. 7s + 10L = 50 15. Write an equation for the situation.

25. Your Turn: Adult tickets cost $20. Student tickets cost $15. The total amount of money brought in from the sale of tickets was $2500. 16. Write an equation for this relation. 17. If 50 adult tickets were sold, how many student tickets were sold?

26. Your turn: It takes 2000 lbs of steel to make a Honda Accord. (2000 lbs per car) (2000 lbs per car) 18. What is the slope? 21. If the total steel used was 100,000 tons, how many cars were built? cars were built? 20. Write an equation that you can use to predict total pounds of steel needed for any given number of cars. pounds of steel needed for any given number of cars. 19. What is y-intercept?

27. Homework Blog worksheet.

28. Your turn: Your budget is $5000. You need to buy wood and concrete. Wood costs $4 per board foot and concrete cost $3 per Wood costs $4 per board foot and concrete cost $3 per 80 pound sack. 80 pound sack. 12. What is the x-axis? 14. Write an inequality that you can use to predict total cost of the wood and the concrete that you can buy. cost of the wood and the concrete that you can buy. 13. What is y-axis? 15. Graph the inequality. 16. If you buy 700 board feet of wood, can you also buy 680 sacks of concrete? 680 sacks of concrete?

29. Inequality Word Problems 4. What is the cost if you don’t buy any nails? Nails cost $5 per pound. Write an inequality showing how many pounds of nails you can buy if the most you can spend is $25. pounds of nails you can buy if the most you can spend is $25. 1.Write an inequality representing pounds of nails you can buy. # lbs of nails bought at most you can spend $100 at most you can spend $100 25 ≥ 5x Slope = ? 2. What are the units of the x-axis ? 3. What are the units of the y-axis ? Total cost in $ 5 ≥ x Can you buy less than 0 lbs Can you buy less than 0 lbs of nails? of nails? 5 ≥ x ≥ 0

30. Standard Form Linear word problems These type usually are total cost of two items. 3. The budget for your party is $50, graph a line that shows all the possible numbers of pizzas and drinks you can buy. 10 pizzas 40 drinks 4.If you buy 5 pizzas, how many drinks can you buy? can you buy?

31. Inequality Word Problems Nails cost $5 per pound. Screws cost $10 per pound. You can spend up to $30. can spend up to $30. 2. Graph the inequalities. Graph the lines. 5x + 10y ≤ 30 x ≥ 0 x ≥ 0 Any combination of pounds of screws or nails in the shaded region will be cost between $0 and $30. shaded region will be cost between $0 and $30. y ≥ 0 y ≥ 0 3 6