The Home Depot Algebra Project. St. Peter Algebra 2016

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The Home Depot Algebra Project St. Peter Algebra 2016 The following project will be done in conjunction with Chapter 3 (pp. 146-217). Please follow all guidelines and complete all assignments.

1 The Home Depot Algebra Project St. Peter Algebra 2016 The following project will be done in conjunction with Chapter 3 (pp ). Please follow all guidelines and complete all assignments. Follow the directions carefully. Is your bedroom too small? Do you have to room with your brother or sister? Is there just not enough space for all your toys, games, devices, and underwear? Good news! You are going to design your very own bedroom. You will be choosing the flooring, paint, lighting, and any extra items you may need, but you will have to stay within your budget and dimensions. Once all of the preliminary work is done, we may take a trip to Home Depot to purchase all of our items. Enjoy the construction of your very own room. 1. On a coordinate plane, please map out your room. Please have any and all corners measure 90. Your room can be no larger than 225 ft 2 and no smaller than 64 ft 2 (your building a bedroom, not a prison cell). On your graph paper, 1 square =1 ft = 1 ft 2. Your room design has to be in each quadrant. Please list the corners as ordered pairs. (10 points) 2. On your coordinate plane, please label the x and y axis and the quadrants. (6 points) 3. Ax + By = C represents a linear function provided that B does not equal 0. The equation 150x + -2y = is a linear function that shows the cost per hour of hiring a construction manager to help you with some of the planning and building. Graph this function. (10 points) 4. Using the data from the graph, answer the following (2 points each): a. What does it cost just to hire this person without him working a single hour? b. If this person works for 10 hours, how much would you have to pay him? c. How much does this person charge per hour? d. Rewrite the above equation in slope-intercept form: 5. From the equation in number 3, can the domain be a negative number? Support your answer. (5 points) 6. Would the equation in number 3 be a continuous or discrete function? Support your answer. (5 points)

2 7. Look at your graph from number 3 and identify the x and y intercepts (4 points). a. -intercept: b. Y-intercept: 8. Fundraising! In all the excitement of building your new room, you forgot that you need to fund this project. You have decided that you can earn a lot of money from that beautiful smile that you have so you are going to sell autographed pictures of yourself. You sell the small autographed pictures (8x10) for $30 and large poster sized autographed pictures (20x24) for $50. You want to earn a quick $600 each week doing this to have enough money to cover all of your expenses. This situation can be modeled by 30x + 50y = 600 where x is the small pictures and y is the large pictures. a. Find the intercepts before you graph it. (4 points) b. Graph this equation. (5 points) c. Give three possibilities for the number of each type of pictures you can sell to earn your $600 each week. (3 points) 9. You have graphed two problems so far. What type of slope did each have (positive, negative, zero, or undefined? Please identify which graph and the type of slope it has by using the number of the graph or some other identification. (5 points) 10. Bad news. You ordered a new light for your new room, but none of the Home Depots in the area had this light in stock. You have to go to the Home Depot in Michigan City, IN which is 200 miles away. Due to construction, you have a longer trip than expected on the way home, and your average speed for the trip is 50mi/hr. Your distance d (in miles) from home is given by d=200-50t where t is the time (in hours) spent driving. Graph the function and identify its domain and range. What is your distance from home after driving for 1.5 hours? (10 points) 11. In order for you to move new furniture into your house to get to your new room, you may have to build a ramp. Conduct the activity on p. 172 in your book and answer the questions (1-6) below (8 points):

12. You have been working hard and decided to treat yourself to a meal at Culvers, where you spent $12.79 (most of which was your concrete mixer dessert).

3 12. You have been working hard and decided to treat yourself to a meal at Culvers, where you spent $12.79 (most of which was your concrete mixer dessert). On your trip back, you decided to graph part of your trip. The data you collected is seen in the graph below. Answer the following (2 each): a. How long did you record your data for: b. What was the rate of change (slope) of your line for the first 10 seconds: c. What happened from point B to point C: d. Describe what happened from point D to point F: e. What was the rate of change (slope) of your line for the last five seconds (point E to point F): f. There is one thing wrong with the graph (it has something to do with the y-axis. Please identify what it is: (2 points) 13. With all of this driving around, your parents have incurred more expense and now the car needs to be repaired. A service station charges $40 per hour for labor plus the cost of parts to repair the car. Parts can either be ordered from the car dealership for $250 or from a warehouse for $200. The equations below give the total repair cost C (in dollars) for a repair that takes t hours using parts from the dealership or from the warehouse. Dealership: C = 40t Warehouse: C = 40t a. Graph both equations in the same coordinate plane. (10 points) b. Use the graphs to find the difference of the costs if the repair takes 3 hours. What if the repair takes 4 hours? What do you notice about the differences of the costs? Explain. (5 points)

4 14. You have done a lot of work so far so it is time for vacation. The amount of vacation v (in hours) that you earn from your parents on this job varies directly with the amount of time t (in weeks) you work. If you work 2 weeks, you earn 3 hours of vacation. (Reminder: a direct variation equation is of the form y = ax, with a not equal to 0.) a. Write a direct variation equation that relates t and v. (5 points) b. How many hours of vacation time do you get in 8 weeks? (5 points) 15. You have a lot of items in your room that you want to keep private so you are looking into room security. SOPP is a home security company that you are looking to hire (Stay Out Private Property). SOPP charges new customers $155 for the installation of security equipment and a monthly fee of $40 (this is for only one room yours). To attract more customers, the company reduces its installation fee to $75. The functions below give the total cost for x months of service. Regular Fee: f(x) = 40x Reduced Fee: g(x) = 40x + 75 Graph both functions in the same coordinate plane. (10 points) How is the graph of the g related to the graph of f? (2 points) 16. You are doing a great job spending money and taking vacations, but now you have to start earning some more income. You decide to start selling tickets for tours through your new room once it is completed. You are going to sell tickets to adults for $5 and to children (16 and under) for $2. The revenue (in dollars) generated from the sale of x tickets is given by a(x) = 5x for adults and c(x) = 2x for children. Graph both functions in the same coordinate plane (10 points). How is the graph of a related to the graph of c? (2 points) 17. Now it is time to start doing some planning for the finishing touches on your project. First of all, you need to figure the total area (in square feet) of your floor. Please show all work (5 points). 18. Next, you need to figure out how many windows and doors you want in your room. On the graph of your floor plan, please add where you want the doors and windows. (5 points)

5 19. For the next part, you have to determine the area of your ceiling and all of the walls in your room for painting. Please list all walls separately. All walls are 8 feet tall. Please record each wall separately and then add together at the end. Reminder: Don t forget to take out the area of the windows and doors. (10 points) a. Area of Ceiling: b. Area of Wall 1: c. Area of Wall 2: d. Area of Wall 3: e. Area of Wall 4: f. Area of Wall 5: g. Area of Wall 6: h. Area of Wall 7: i. Area of Wall 8: j. Total Area: 20. For the next part of this project, you will need to pick out your door(s), windows, paint color, amount of paint (1 primer and 2 coats of paint), lighting, and amount of carpeting (or other flooring) needed (don t forget the padding). (Assume all installation will be done by your builder who your parents hired and will pay.) You will need to figure your total cost. Your budgeted amount is $1000. You want to try to stay within your budget if you can. Points will not be deducted if you go over budget, but you will get extra points if you are under budget (50 points). (See spreadsheet on next page.) 21. Finally, you need to have a written or typed paper (minimum 3 paragraphs) describing your newly designed room. Your description must fit with what you purchased for your room. You will be graded on the conventions of writing but the majority of your grade will be on how well you describe your room. (50 points)

6 Door ITEM BRAND/MODEL COLOR DIMENSIONS COST QUANTITY TOTAL Door Hardware (Knobs) Primer (one coat all walls) Paint*** (two coats) Ceiling Paint (two coats) Paint Brushes Floor Covering Padding Lighting Window Window Bulbs Other Add 6% Tax Total ***Please bring back paint chip cards for the color of your room (5 points)

Answers for the lesson Plot Points in a Coordinate Plane

LESSON 3.1 Answers for the lesson Plot Points in a Coordinate Plane Skill Practice 1. 5; 23 2. No; the point could lie in either Quadrant II or Quadrant IV. 3. (3, 22) 4. (, 21) 5. (4, 4) 6. (24, 3) 7.