module 2- a1.2.2 - coordinate geometry 5.pdfthree linear equations are shown below. y1 = 2x 5 y2 = 1...

Module 2- A1.2.2 - Coordinate Geometry

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 ` in the accompanying diagram?

A. y = 2x + 2 B. y = 2x − 4 C. y = −2x − 4 D. y = −2x + 2

3. Which graph represents the equation x = −3?

A. B. C. D.

page1

4. What is the equation of the line in the accompanying graph?

A. 2y = x − 2 B. y = 12x + 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 Module 2- A1.2.2 - Coordinate Geometry

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.


9. Three linear equations are shown below.

y1 = −2x − 5

y2 = − 12x − 5

y3 = 3x − 5

Which statement about the three linear equations is incorrect?

A. All three equations have the same slope. B. Equations y1 and y2 have negative slopes.

C. All three equations have the same y-intercept. D. Equations y2 and y3 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. 5

11. What are the y-intercept and the slope of the graph of the following equation?

−2x + 4y = 8

A. y-intercept: 8slope: −2

B. y-intercept: 8slope: 2

C. y-intercept: 2slope: − 1

2

D. y-intercept: 2slope: 1

2

12. What is the y-intercept of the graph of the equation 3x + 6y = 18

A. −6 B. −3 C. 3 D. 6


13. What are the y-intercept and the slope of the graph below?

A. y-intercept: 3slope: 2

3

B. y-intercept: 3slope: − 3

2

C. y-intercept: -3slope: 3

2

D. y-intercept: -3slope: − 2

3

14. Which graph contains the points given in the table below?

x y

−2 3

−1 1

1 −3

A. B. C. D.


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.


17. Which of the following lines appears to have a y-intercept of 4 and a slope of 13?

A. B.

C. D.


18. What is the apparent x-intercept of the line graphed below?

A. 2 B. 1 C. −1 D. −2

19. 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.


21. What is the slope of the line represented by the equation below?

3x + 2y = −8

A. −3 B. − 32 C. 3

2 D. 3

22. What is the y-intercept of the line represented by the equation below?

10x + 5y = 20

A. −4 B. −2 C. 2 D. 4

23. 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


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 = − 35 and b = − 4

5 B. m = − 53 and b = −4 C. m = − 4

5 and b = − 35 D. m = − 3

5 and b = 4

26. Which statement best describes the similarities of the graphs 2y = 5x + 67 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. 53 B. 3

5 C. −35 D. −5

3


28. The line passing through points (x, 4) and (4,−5) is perpendicular to a line with a slope of − 73 . What is the value

of x?

A. −17 B. 17 C. 55

7 D. 25

29. 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 first30 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)

0 10

2 2

4 −6

6 −14

What is the slope of f (x)?

A. −8 B. −4 C. 4 D. 8


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. 27 B. 4

6 C. 189 D. 7

2


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)


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

4 5

7 7

10 9

13 11

B. x y

4 56

5 56

6 56

7 56

C. x y

4 124

8 267

12 407

16 551

D. x y

14 58

24 47

34 36

44 25


37. A trapezoid is shown on the grid below.

What is the slope of each base of the trapezoid?

A. 14 B. 1

2 C. 1 D. 4

38. Look at the graph below.

Which line on the graph has a slope of 53?

A. `1 B. `2 C. `3 D. `4


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 theslope of

−−−UR ?

A. −2 B. − 12 C. 1

2 D. 2


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 isparallel to the roof. What is the slope of the ceiling?

A. 37 B. 3

4 C. 43 D. 7

4

44. Use the equations below to answer the following question.

y = 23x − 9

y = 23x + 3

The equations describe

A. parallel lines. B. the same line.

C. perpendicular lines. D. intersecting, not perpendicular lines.


45. Amelia recorded the time it took for candles of different lengths to burn out. Her results are shown in the tablebelow.

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 wasthe 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.


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 thenumber of items sold.

Clothing Shop Profits

Number ofSweaters Sold

Amount of Profit(in dollars)

10

15

25

Number ofPairs of Jeans Sold

Amount of Profit(in dollars)

10

15

25

Part B What is the amount of profit made from selling one sweater? In the space below, show your work andwrite 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 moreprofit? 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 $


47. Each month, Jean’s phone company charges her $10.00 for the first 30 minutes of phone calls and $0.25 for eachadditional 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 howyou 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.


48. The table below shows the student enrollment at Eastside High School for five different years from 1960 to 2000.

Year Enrollment

1960 185

1970 315

1980 577

1990 930

2000 1362

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 tothe 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 monthto 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.


50. A biologist conducted a study of the population of frogs in a large pond near Norwich. The population has beendecreasing as shown in the table below.

On the grid below, make a scatter-plot that shows the information from the table. Be sure to title your graph,choose an appropriate scale and label your axes.

Based on the pattern in the table or on your graph, what will be the approximate frog population in 2004? Showyour work or explain how you found your answer.


51. The table below shows the population of New London County, Connecticut, from 1950 to 2000.

Year Population

1950 145,000

1960 186,000

1970 230,000

1980 238,000

1990 255,000

2000 259,000

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 2010. Explain how you foundyour answer.


52. The Main Street Cinema is planning to add a coffee bar. The owners estimate that the fixed monthly expenseswill be $2,700. Additionally, each cup of coffee will cost $0.25 to make and will be sold for $0.95. The ownersestimate 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 showhow you found your answer.

c) The owners need a formula to calculate monthly profit or loss. Using the variables listed below, write aformula 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 nearwhere 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 andn 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 atTammy’s Take-Out than at Hector’s To-Go? Remember that Elena always buys a bottle of juice with hersalad. Show or explain how you found your answer.


54. Suppose that a piano costs $5000 and loses 20% of its value each year. The table below shows the value, v, of apiano after, t, years.

Value of the Piano

Number of YearsSince Purchase

(t)

Value of Piano(v)

0 $5000

1 $4000

2 $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 obtainedyour 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, thenumber of miles traveled.

In New York City, Quinn pays a fixed taxi fare of $1.50 per ride, plus 25/c per 110 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, thenumber of miles traveled.

c) On a recent trip Quinn noticed that the total number of miles traveled by taxi from the airport to the hotelwas the same in each of the two cities. Before tips were added, his taxi fare to the hotel in New York Citywas $12.20 more than his taxi fare to the hotel in Chicago. What was the distance from the airport to thehotel in each city? Show or explain how you got your answer.


56. Guy publishes a small monthly magazine called Sea Surfer. His only expenses each month are $2.10 for printingand 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 magazinecopies 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 ineach issue.

b) Guy has sold $1140 worth of advertising space for the July issue of Sea Surfer. Write an equation thatexpresses 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 $900worth 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 tosell 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 thechecking account.

a) What was the total amount of money in Laurie’s checking account at the end of week 5? Show or explainhow 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 = 0corresponds 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 foryour graph.

c) Write an equation that represents the line that passes through all the points plotted in part (b). Show orexplain 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 ofthis problem.


58. The workers at a company received a bonus this year. The table below shows the numbers of years some of theworkers have been employed at the company and the bonus each worker received.

Years Employed andBonuses Received

Worker’sName

Numberof YearsEmployed

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 aredefined 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 foryour 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 companyfor 10 years should expect to receive. Show or explain how you got your answer.


59. The table below shows the distances, in miles, and the lowest-priced airfares, in dollars, of flights from Baltimoreto various destinations.

LOWEST-PRICED AIRFARESFROM 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) traveledand 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.


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 2010. Show your work.


Problem-Attic format version 4.4.172c_ 2011–2013 EducAide Software

Licensed for use by Tammie WilkesTerms of Use at www.problem-attic.com

Module 2- A1.2.2 - Coordinate Geometry 04/22/2013

1.Answer: C

2.Answer: B

3.Answer: B

4.Answer: D

5.Answer: A

6.Answer: A

7.Answer: D

8.Answer: D

9.Answer: A

10.Answer: B

11.Answer: D

12.Answer: C

13.Answer: C

14.Answer: B

15.Answer: A

16.Answer: A

17.Answer: A

18.Answer: D

19.Answer: A

20.Answer: A

21.Answer: B

22.Answer: D

23.Answer: D

24.Answer: B

25.Answer: A

26.Answer: A

27.Answer: A

28.Answer: D

29.Answer: It was faster

30.Answer: B

31.Answer: C

32.Answer: D

33.Answer: B

34.Answer: C

35.Answer: C

36.Answer: D

37.

38.

39.Answer: B

Teacher’s Key Page 2

40.Answer: B

41.Answer: D

42.Answer: C

43.Answer: C

44.Answer: A

45.

46.

47.Answer: ;

;

$27.50 100 minutes - 30 minutes =70 minutes 70 × $0.25 = $17.50$17.50 + $10.00 = $27.50; K = totalnumber of minutes T = total billT = 10 + (K − 30)(0.25)

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.Answer: Part A: Student has drawn a line as

close to the points as possible on aslope that follows the trend of thepoints.

Part B: Correct equation derivedthrough calculator- use of linearcorrelation and regression formula.

Why: I looked for points on the lineof best fit that were easiest to identify.I then used the slope formula to findthe slope of that line. I found thelocation of the y-intercept by lookingat my line of best fit. I substitutedthe slope and the y-intercept in theequation y = mx + b to get the equationfor the line.

Part C: Correct answer based onreasonable equation shown in part B

module 2- a1.2.2 - coordinate geometry 5.pdfthree linear equations are shown below. y1 = 2x 5 y2 = 1...

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