Module 2- A Coordinate Geometry. 1. What is an equation of the line whose graph is shown? A. y = x B. y = 2x C. y = x D.

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1 Name: Date: 1. What is an equation of the line whose graph is shown? A. y = x B. y = 2x C. y = x D. y = 2 2. Which is an equation for line l in the accompanying diagram? A. y = 2x + 2 B. y = 2x 4 C. y = 2x 4 D. y = 2x Which graph represents the equation x = 3? A. B. C. D. page1

2 4. What is the equation of the line in the accompanying graph? A. 2y = x 2 B. y = 2 1 x + 1 C. y = 2x 2 D. y = 2x 2 5. Which graph represents the graph of the equation x = 2? A. B. C. D. 6. Which graph represents the equation x = 2? A. B. C. D. page2

3 7. Which of these lines has a slope of 3? A. B. C. D. 8. Which statement is true? A. All vertical lines have a slope of zero. B. All vertical lines have a positive slope. C. All vertical lines have a negative slope. D. All vertical lines have an undefined slope. page3

4 9. Three linear equations are shown below. y 1 = 2x 5 y 2 = 2 1x 5 y 3 = 3x 5 Which statement about the three linear equations is incorrect? A. All three equations have the same slope. B. Equations y 1 and y 2 have negative slopes. C. All three equations have the same y-intercept. D. Equations y 2 and y 3 have the same y-intercept. 10. What is the y-intercept for the graph of the equation 3x 5y = 15? A. 5 B. 3 C. 3 D What are the y-intercept and the slope of the graph of the following equation? 2x + 4y = 8 A. y-intercept: 8 slope: 2 B. y-intercept: 8 slope: 2 C. y-intercept: 2 slope: 1 2 D. y-intercept: 2 slope: What is the y-intercept of the graph of the equation 3x + 6y = 18 A. 6 B. 3 C. 3 D. 6 page4

5 13. What are the y-intercept and the slope of the graph below? A. y-intercept: 3 slope: 2 3 B. y-intercept: 3 slope: 3 2 C. y-intercept: -3 slope: 3 2 D. y-intercept: -3 slope: Which graph contains the points given in the table below? x y A. B. C. D. page5

6 15. Which of the following shows the graph of a line with positive slope? A. B. C. D. 16. Which of the lines graphed below has the greatest positive slope? A. B. C. D. page6

7 17. Which of the following lines appears to have a y-intercept of 4 and a slope of 1 3? A. B. C. D. page7

8 18. What is the apparent x-intercept of the line graphed below? A. 2 B. 1 C. 1 D Which of the following describes the slope of a horizontal line on the coordinate plane? A. zero B. positive C. negative D. undefined 20. In which of the following graphs does line k best represent a line with a slope of 0? A. B. C. D. page8

9 21. What is the slope of the line represented by the equation below? 3x + 2y = 8 A. 3 B. 3 2 C. 3 2 D What is the y-intercept of the line represented by the equation below? 10x + 5y = 20 A. 4 B. 2 C. 2 D Four line segments are shown on the coordinate grid below. Which of the line segments has a slope of 0? A. PQ B. QR C. RS D. ST page9

10 24. Six points are plotted on the coordinate grid below. Which two points lie on a line with a slope closest to zero? A. N and J B. N and K C. P and L D. P and Q 25. What are the slope, m, and the y-intercept, b, of a line that passes through the points ( 3, 1) and (7, 5)? A. m = 3 5 and b = 4 5 B. m = 5 3 and b = 4 C. m = 4 5 and b = 3 5 D. m = 3 5 and b = Which statement best describes the similarities of the graphs 2y = 5x and 2y = 3x + 6 7? A. The y-intercepts are the same. B. The slopes are the same. C. The x-intercepts are the same. D. The graphs are identical. 27. What is the slope of the line that passes through the points (1, 3) and (4, 2)? A. 3 B. 5 C. 5 D. 3 page10

11 28. The line passing through points (x, 4) and (4, 5) is perpendicular to a line with a slope of 7 3. What is the value of x? A. 17 B. 1 7 C D The graph below shows the distance Ben skied during a 50-minute practice. How does Ben s speed during the last 20 minutes of the practice compare with his speed during the first 30 minutes? Explain your answer. 30. The table below shows the relationship between x and f (x) for the linear function f (x). x f (x) What is the slope of f (x)? A. 8 B. 4 C. 4 D. 8 page11

12 31. The equation below is used to find (x, y) coordinates. y = 3x + 2 Which coordinates could be found using the equation above? A. B. C. D. 32. Bennie is using this pattern to make stars for an Alaska state flag. What is the slope of line segment AB in Bennie s pattern? A. 2 7 B. 4 6 C D. 7 2 page12

13 33. Which statement is true about the slope of line AC? A. The slope is the ratio of the x and y intercepts. B. The slope is the same between any two points on the line. C. The slope between point A and point B is greater than the slope between point B and point C. D. The slope between point A and point C is greater than the slope between point A and point B. 34. Which point lies on the line represented by the equation below? 5x + 4y = 22 A. ( 2, 11 4 ) B. ( 1, 17 4 ) C. (2, 3) D. (6, 2) page13

14 35. Use the graph to answer the question. Which statement is true about the lines on the graph? A. They have the same slope and the same y-intercept. B. They have the same slope but different y-intercepts. C. They have different slopes but the same y-intercept. D. They have different slopes and different y-intercepts. 36. Which table shows a decreasing linear relationship? A. x y B. x y C. x y D. x y page14

15 37. A trapezoid is shown on the grid below. What is the slope of each base of the trapezoid? A. 1 4 B. 1 2 C. 1 D Look at the graph below. Which line on the graph has a slope of 5 3? A. l 1 B. l 2 C. l 3 D. l 4 page15

16 39. The lines graphed on the coordinate plane below intersect to form polygon PRSTV. Which side of polygon PRSTV is on a line with a slope of 3? A. PR B. ST C. TV D. VP 40. On the graph below, points S, Q, U, and R are connected to form a square. The slope of SQ is 1 2. What is the slope of UR? A. 2 B. 1 2 C. 1 2 D. 2 page16

17 41. The relationship between the two lines on the graph can best be described as. A. vertical B. horizontal C. parallel D. perpendicular 42. Determine the slope of line with points located at ( 3, 2) and (1, 2). A. 2 B. 5 C. 0 D. Undefined 43. The roof of a house rises 4 feet vertically for every 3 feet it runs horizontally. The ceiling inside the house is parallel to the roof. What is the slope of the ceiling? A. 3 7 B. 3 4 C. 4 3 D Use the equations below to answer the following question. y = 2 3 x 9 y = 2 3 x + 3 The equations describe A. parallel lines. B. the same line. C. perpendicular lines. D. intersecting, not perpendicular lines. page17

18 45. Amelia recorded the time it took for candles of different lengths to burn out. Her results are shown in the table below. Part A On the grid below, create a scatterplot of her data and draw a line of best fit for the data. Be sure to title the scatterplot label each axis use appropriate scales Part B On the line below, write the equation for your line of best fit. Part C The next candle that Amelia tested burned for one hour. According to your line of best fit, how long was the candle? In the space below, explain or show how you found your answer and write your answer on the line. inches Part D On the lines below, explain what the slope represents within the context of this problem. page18

19 46. Study the graph below. The graph shows the profit a clothing shop makes from selling sweaters and pairs of jeans. Part A Complete the tables below by using the information from the graph to show the amount of profit for the number of items sold. Clothing Shop Profits Number of Sweaters Sold Amount of Profit (in dollars) Number of Pairs of Jeans Sold Amount of Profit (in dollars) Part B What is the amount of profit made from selling one sweater? In the space below, show your work and write your answer on the line. $ Part C In one day, the shop sold 20 sweaters and 30 pairs of jeans. The sale of which of these items made more profit? In the space below, show your work to find the difference in profit and write your answers on the lines. made in profit Difference in profit $ page19

20 47. Each month, Jean s phone company charges her $10.00 for the first 30 minutes of phone calls and $0.25 for each additional minute. Part A Use the information above to help you complete this table. Part B On the grid below, construct a graph showing the cost of Jean s phone calls. Be sure to title your graph label each axis Part C What is Jean s phone bill if she uses her phone for 100 minutes? In the space below, explain or show how you found your answer and write your answer on the line. $ Part D In the space below, write a rule or equation showing how Jean can find her total bill each month. page20

21 48. The table below shows the student enrollment at Eastside High School for five different years from 1960 to Year Enrollment a) Construct a scatter plot of the data in the table. b) Based on the pattern in your graph, what do you predict the school s enrollment will be in 2001? c) Explain how you arrived at your prediction. 49. Advance Tickets Sold The scatterplot below shows the number of advance tickets sold each day for a month for a new musical coming to the Bushnell Theater in Hartford. The line of the best fit has been drawn on the scatterflot. Write an equation that relates x, the day of the month to y, the number of tickets sold according to the line of best fit. Explain what the numbers in your equation mean in terms of the tickets sold. page21

22 50. A biologist conducted a study of the population of frogs in a large pond near Norwich. The population has been decreasing as shown in the table below. On the grid below, make a scatter-plot that shows the information from the table. choose an appropriate scale and label your axes. Be sure to title your graph, Based on the pattern in the table or on your graph, what will be the approximate frog population in 2004? Show your work or explain how you found your answer. page22

23 51. The table below shows the population of New London County, Connecticut, from 1950 to Year Population , , , , , ,000 a) Make a scatter plot of the data in the grid below. Be sure to label the axes. b) Make a reasonable prediction for the population in New London County in Explain how you found your answer. page23

24 52. The Main Street Cinema is planning to add a coffee bar. The owners estimate that the fixed monthly expenses will be $2,700. Additionally, each cup of coffee will cost $0.25 to make and will be sold for $0.95. The owners estimate that they will sell 3,000 cups of coffee each month. a) What would be their monthly profit or loss on selling coffee? Explain or show how you found your answer. b) What price per cup would they have to charge to break even (neither a profit nor a loss)? Explain or show how you found your answer. c) The owners need a formula to calculate monthly profit or loss. Using the variables listed below, write a formula to determine their monthly profit or loss. Fixed monthly expenses: F Cost to make each cup: C Selling price of each cup: S Number of cups sold in a month: N Monthly profit or loss: P 53. When Elena works on Saturdays, she buys a salad and juice for lunch. There are two take-out restaurants near where she works. The prices in the two restaurants are given below. a) How many ounces of salad, together with a bottle of juice, can Elena buy at Hector s To-Go for $4.50? b) Write an equation that shows the cost, C, of Elena s lunch at Hector s To-Go if she buys a bottle of juice and n ounces of salad. c) Graph the equation you wrote in part b. Use the horizontal axis for the number of ounces, with each increment representing one ounce. Use the vertical axis for cost, with each increment representing 50/c. d) What are the different amounts of salad that Elena can buy so her complete lunch is less expensive at Tammy s Take-Out than at Hector s To-Go? Remember that Elena always buys a bottle of juice with her salad. Show or explain how you found your answer. page24

25 54. Suppose that a piano costs $5000 and loses 20% of its value each year. The table below shows the value, v, of a piano after, t, years. Value of the Piano Number of Years Since Purchase (t) Value of Piano (v) 0 $ $ $3200 a) Complete the missing values. Show or explain how you obtained your answers. b) Using the data in your table, draw and label a graph that shows the relationship between t and v. c) After how many years will the piano first be valued at less than $500? Show or explain how you obtained your answer. d) What will the value of the piano be after 16 years? Show or explain how you obtained your answer. 55. Quinn works in Chicago and in New York City. He travels by taxi in each of the two cities. In Chicago, he pays a fixed taxi fare of $1.90 per ride, plus $1.60 per mile traveled. a) Write an equation that expresses f, Quinn s total fare for a taxi ride in Chicago, as a function of m, the number of miles traveled. In New York City, Quinn pays a fixed taxi fare of $1.50 per ride, plus 25/c per 1 10 mile traveled. b) Write an equation that expresses f, Quin s total fare for a taxi ride in New York City, as a function of m, the number of miles traveled. c) On a recent trip Quinn noticed that the total number of miles traveled by taxi from the airport to the hotel was the same in each of the two cities. Before tips were added, his taxi fare to the hotel in New York City was $12.20 more than his taxi fare to the hotel in Chicago. What was the distance from the airport to the hotel in each city? Show or explain how you got your answer. page25

26 56. Guy publishes a small monthly magazine called Sea Surfer. His only expenses each month are $2.10 for printing and shipping each copy and $4500 for paying writers and editors. a) Write an equation that expresses t, Guy s total expenses each month, in terms of n, the number of magazine copies he prints and ships. Guy s revenue comes from the sale of the magazine at $3.50 per copy and the sale of advertising space in each issue. b) Guy has sold $1140 worth of advertising space for the July issue of Sea Surfer. Write an equation that expresses R, Guy s total revenue in July, in terms of n, the number of copies of the July issue he sells. c) What would Guy s profit (or loss) be for a month in which he sells 1800 copies of the magazine and $900 worth of advertising space? Show or explain how you got your answer. d) Based on your results in parts a and b, how many copies of the July issue of Sea Surfer will Guy have to sell in order for his revenue to equal his expenses? Show or explain how you got your answer. 57. Laurie s parents gave her $25 to open a checking account. At the end of each week after the account was opened, Laurie deposited $20 into her checking account. No other money was deposited into or withdrawn from the checking account. a) What was the total amount of money in Laurie s checking account at the end of week 5? Show or explain how you got your answer. b) Plot six points with coordinates (x, y), in which x and y are defined as follows: x = the number of weeks since the account was opened (in whole numbers from 0 through 5), where x = 0 corresponds to the opening of the account y = the total amount of money in the account at the end of week x Be sure to label the x-axis and y-axis, indicate the scale on each axis, and include a title for your graph. c) Write an equation that represents the line that passes through all the points plotted in part (b). Show or explain how you determined your equation. d) For the line represented by your equation in part (c), explain the meaning of the y-intercept in the context of this problem. page26

27 58. The workers at a company received a bonus this year. The table below shows the numbers of years some of the workers have been employed at the company and the bonus each worker received. Years Employed and Bonuses Received Worker s Name Number of Years Employed Bonus Martinez 2 $250 Leung 4 $500 Sagafi 1 $100 Chandler 3 $200 Parker 6 $600 Vittel 5 $450 a) What is the range of the bonuses in the table? Show or explain how you got your answer. b) Make a scatterplot of the data in the table by plotting points with coordinates (x, y), where x and y are defined as follows: x = number of years a worker has been employed y = bonus ($) received by that worker Be sure to label the x-axis and y-axis, indicate the scale on each axis, and provide a title for your scatterplot. c) On the grid, draw a line that approximates the line of best fit (trend line) for your scatterplot. d) Use your trend line from part (c) to predict the bonus that a worker who has been employed at the company for 10 years should expect to receive. Show or explain how you got your answer. page27

28 59. The table below shows the distances, in miles, and the lowest-priced airfares, in dollars, of flights from Baltimore to various destinations. LOWEST-PRICED AIRFARES FROM BALTIMORE Destination Distance (in miles) Airfare Atlanta 576 $164 Boston 370 $124 Chicago 612 $143 Dallas 1,216 $260 Detroit 409 $161 Denver 1,502 $216 Miami 946 $180 New York 189 $108 St. Louis 737 $180 The data from the table is graphed on the scatter plot on the next page. The data from the previous page has been graphed below. a) Write an equation for a line of best fit that can represent the relationship between the distance (d) traveled and the lowest-priced airfare (f ). b) Graph the equation for your line of best fit on a scatter plot. c) According to your equation, what is the cost of a plane ticket to Orlando, which is 790 miles from Baltimore? Use mathematics to justify your answer. page28

29 60. The population of Lanville has been increasing since 1980, as shown in the scatter plot below. a) Draw a line of best fit on the coordinate plane for the points shown on the Lanville population scatter plot. You may use the regression formula or estimate the line. b) Write an equation for the line you drew in part A. Show all your work. Explain why you did each step. c) Using the equation you wrote in part B, predict the population of Lanville in Show your work. page29

30 Problem-Attic format version c EducAide Software Licensed for use by Tammie Wilkes Terms of Use at 04/22/ C 20. A 2. B 21. B 3. B 22. D 4. D 23. D 5. A 24. B 6. A 25. A 7. D 26. A 8. D 27. A 9. A 28. D 10. B 29. It was faster 11. D 30. B 12. C 31. C 13. C 32. D 14. B 33. B 15. A 34. C 16. A 35. C 17. A 36. D D A B

31 B D C C A 47. ; ; Teacher s Key Page 2 Part A: Student has drawn a line as close to the points as possible on a slope that follows the trend of the points. Part B: Correct equation derived through calculator- use of linear correlation and regression formula. Why: I looked for points on the line of best fit that were easiest to identify. I then used the slope formula to find the slope of that line. I found the location of the y-intercept by looking at my line of best fit. I substituted the slope and the y-intercept in the equation y = mx + b to get the equation for the line. Part C: Correct answer based on reasonable equation shown in part B $ minutes - 30 minutes = 70 minutes 70 $0.25 = $17.50 $ $10.00 = $27.50; K = total number of minutes T = total bill T = 10 + (K 30)(0.25)