4. (6, 3), (7, 4) 5. ( 9, 3), ( 7, 5) 6. (6, 2), (5, 4) 7. (7, 4), (4, 8) 8. ( 7, 8), ( 7, 5) 9. (5, 9), (3, 9)

Transcription

1 Algebra 1 Section 3.3 Worksheet Find the slope of the line that passes through each pair of points (6, 3), (7, 4) 5. ( 9, 3), ( 7, 5) 6. (6, 2), (5, 4) 7. (7, 4), (4, 8) 8. ( 7, 8), ( 7, 5) 9. (5, 9), (3, 9) 10. (15, 2), ( 6, 5) 11. (3, 9), ( 2, 8) 12. ( 2, 5), (7, 8) 13. (12, 10), (12, 5) 14. (0.2, 0.9), (0.5, 0.9) , 4 3, 1 3, 2 3 Find the value of r so the line that passes through each pair of points has the given slope. 16. ( 2, r), (6, 7), m = ( 4, 3), (r, 5), m = ( 3, 4), ( 5, r), m = ( 5, r), (1, 3), m = (1, 4), (r, 5), m undefined 21. ( 7, 2), ( 8, r), m = (r, 7), (11, 8), m = (r, 2), (5, r), m = ROOFING The pitch of a roof is the number of feet the roof rises for each 12 feet horizontally. If a roof has a pitch of 8, what is its slope expressed as a positive number? 25. SALES A daily newspaper had 12,125 subscribers when it began publication. Five years later it had 10,100 subscribers. What is the average yearly rate of change in the number of subscribers for the five-year period? 26. HIGHWAYS Roadway signs such as the one below are used to warn drivers of an upcoming steep down grade that could lead to a dangerous situation. What is the grade, or slope, of the hill described on the sign?

2 27. AMUSEMENT PARKS The SheiKra roller coaster at Busch Gardens in Tampa, Florida, features a 138-foot vertical drop. What is the slope of the coaster track at this part of the ride? Explain. 28. CENSUS The table shows the population density for the state of Texas in various years. Find the average annual rate of change in the population density from 2000 to Population Density Year People Per Square Mile Source: Bureau of the Census, U.S. Dept. of Commerce 29. REAL ESTATE A realtor estimates the median price of an existing single-family home in Cedar Ridge is $221,900. Two years ago, the median price was $195,200. Find the average annual rate of change in median home price in these years. 30. COAL EXPORTS The graph shows the annual coal exports from U.S. mines in millions of short tons. Source: Energy Information Association a. What was the rate of change in coal exports between 2001 and 2002? b. How does the rate of change in coal exports from 2005 to 2006 compare to that of 2001 to 2002? c. Explain the meaning of the part of the graph with a slope of zero.

3 Algebra 1 Section 4.3 Worksheet Write an equation in point-slope form for the line that passes through each point with the given slope. 1. (2, 2), m = 3 2. (1, 6), m = 1 3. ( 3, 4), m = 0 4. (1, 3), m = ( 8, 5), m = (3, 3), m = 1 3 Write each equation in standard form. 7. y 11 = 3(x 2) 8. y 10 = (x 2) 9. y + 7 = 2(x + 5) 10. y 5 = 3 (x + 4) 11. y + 2 = 3 (x + 1) 12. y 6 = 4 (x 3) y + 4 = 1.5(x + 2) 14. y 3 = 2.4(x 5) 15. y 4 = 2.5(x + 3) Write each equation in slope-intercept form. 16. y + 2 = 4(x + 2) 17. y + 1 = 7(x + 1) 18. y 3 = 5(x + 12) 19. y 5 = 3 2 (x + 4) 20. y 1 4 = 3(x ) 21. y 2 3 = 2(x 1 4 ) 22. CONSTRUCTION A construction company charges $15 per hour for debris removal, plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of service is $195. a. Write the point-slope form of an equation to find the total fee y for any number of hours x. b. Write the equation in slope-intercept form. c. What is the fee for the use of a trash dumpster? 23. MOVING There is a daily fee for renting a moving truck, plus a charge of $0.50 per mile driven. It costs $64 to rent the truck on a day when it is driven 48 miles. a. Write the point-slope form of an equation to find the total charge y for a one-day rental with x miles driven. b. Write the equation in slope-intercept form. c. What is the daily fee? 24. BICYCLING Harvey rides his bike at an average speed of 12 miles per hour. In other words, he rides 12 miles in 1 hour, 24 miles in 2 hours, and so on. Let h be the number of hours he rides and d be distance traveled. Write an equation for the relationship between distance and time in point-slope form. 25. GEOMETRY The perimeter of a square varies directly with its side length. The point-slope form of the equation for this function is y 4 = 4(x 1). Write the equation in standard form.

4 26. NATURE The frequency of a male cricket s chirp is related to the outdoor temperature. The relationship is expressed by the equation T = n + 40, where T is the temperature in degrees Fahrenheit and n is the number of chirps the cricket makes in 14 seconds. Use the information from the graph below to write an equation for the line in point-slope form. 27. CANOEING Geoff paddles his canoe at an average speed of 3.5 miles per hour. After 5 hours of canoeing, Geoff has traveled 18 miles. Write an equation in point-slope form to find the total distance y for any number of hours x. 28. AVIATION A jet plane takes off and consistently climbs 20 feet for every 40 feet it moves horizontally. The graph shows the trajectory of the jet. a. Write an equation in point-slope form for the line representing the jet s trajectory. b. Write the equation from part a in slope -intercept form. c. Write the equation in standard form.

5 Algebra 1 Section 4.2 Worksheet Write an equation of the line that passes through the given point and has the given slope ( 5, 4); slope 3 5. (4, 3); slope (1, 5); slope (3, 7); slope , 5 2 ; slope (5, 0); slope 0 Write an equation of the line that passes through each pair of points (0, 4), (5, 4) 14. ( 4, 2), (4, 0) 15. ( 2, 3), (4, 5) 16. (0, 1), (5, 3) 17. ( 3, 0), (1, 6) 18. (1, 0), (5, 1) 19. DANCE LESSONS The cost for 7 dance lessons is $82. The cost for 11 lessons is $122. Write a linear equation to find the total cost C for l lessons. Then use the equation to find the cost of 4 lessons. 20. WEATHER It is 76 F at the 6000-foot level of a mountain, and 49 F at the 12,000-foot level of the mountain. Write a linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet. 21. FUNDRAISING Yvonne and her friends held a bake sale to benefit a shelter for homeless people. The friends sold 22 cakes on the first day and 15 cakes on the second day of the bake sale. They collected $88 on the first day and $60 on the second day. Let x represent the number of cakes sold and y represent the amount of money made. Find the slope of the line that would pass through the points given.

6 22. JOBS Mr. Kimball receives a $3000 annual salary increase on the anniversary of his hiring if he receives a satisfactory performance review. His starting salary was $41,250. Write an equation to show k, Mr. Kimball s salary after t years at this company if his performance reviews are always satisfactory. 23. CENSUS The population of Laredo, Texas, was about 215,500 in It was about 123,000 in If we assume that the population growth is constant and t represents the number of years after 1990, write a linear equation to find p, Laredo s population for any year after WATER Mr. Williams pays $40 a month for city water, no matter how many gallons of water he uses in a given month. Let x represent the number of gallons of water used per month. Let y represent the monthly cost of the city water in dollars. What is the equation of the line that represents this information? What is the slope of the line? 25. SHOE SIZES The table shows how women s shoe sizes in the United Kingdom compare to women s shoe sizes in the United States. Women s Shoe Sizes a. Write a linear equation to determine any U.S. size y if you are given the U.K. size x. U.K U.S Source: DanceSport UK b. What are the slope and y-intercept of the line? c. Is the y-intercept a valid data point for the given information?

7 Algebra 1 Section 4.1 Worksheet Write an equation of a line in slope-intercept form with the given slope and y-intercept. 1. slope: 1, y-intercept: 3 2. slope: 3, y-intercept: slope: 1.5, y-intercept: 1 4. slope: 2.5, y-intercept: 3.5 Write an equation in slope-intercept form for each graph shown Graph each equation. 8. y = 1 x y = 2x x + 3y = WRITING Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished. a. Write an equation to find the total number of pages P written after any number of months m. Carla s Novel b. Graph the equation on the grid at the right. c. Find the total number of pages written after 5 months. 12. SAVINGS Wade s grandmother gave him $100 for his birthday. Wade wants to save his money to buy a new MP3 player that costs $275. Each month, he adds $25 to his MP3 savings. Write an equation in slope-intercept form for x, the number of months that it will take Wade to save $275.

8 13. CAR CARE Suppose regular gasoline costs $2.76 per gallon. You can purchase a car wash at the gas station for $3. The graph of the equation for the cost of x gallons of gasoline and a car wash is shown below. Write the equation in slope-intercept form for the line. 14. ADULT EDUCATION Angie s mother wants to take some adult education classes at the local high school. She has to pay a onetime enrollment fee of $25 to join the adult education community, and then $45 for each class she wants to take. The equation y = 45x + 25 expresses the cost of taking x classes. What are the slope and y-intercept of the equation? 15. BUSINESS A construction crew needs to rent a trench digger for up to a week. An equipment rental company charges $40 per day plus a $20 non-refundable insurance cost to rent a trench digger. Write and graph an equation to find the total cost to rent the trench digger for d days. 16. ENERGY From 2002 to 2005, U.S. consumption of renewable energy increased an average of 0.17 quadrillion BTUs per year. About 6.07 quadrillion BTUs of renewable power were produced in the year a. Write an equation in slope-intercept form to find the amount of renewable power P (quadrillion BTUs) produced in year y between 2002 and b. Approximately how much renewable power was produced in 2005? c. If the same trend continues from 2006 to 2010, how much renewable power will be produced in the year 2010

9 Algebra 1 Section 5.6 Worksheet Determine which ordered pairs are part of the solution set for each inequality. 1. 3x + y 6, {(4, 3), ( 2, 4), ( 5, 3), (3, 3)} 2. y x + 3, {(6, 3), ( 3, 2), (3, 2), (4, 3)} 3. 3x 2y < 5, {(4, 4), (3, 5), (5, 2), ( 3, 4)} Graph each inequality. 4. 2y x < x 2y y > 2x 3 Use a graph to solve each inequality x > 2 3 x > 2 x MOVING A moving van has an interior height of 7 feet (84 inches). You have boxes in 12 inch and 15 inch heights, and want to stack them as high as possible to fit. Write an inequality that represents this situation. 11. BUDGETING Satchi found a used bookstore that sells pre-owned DVDs and CDs. DVDs cost $9 each, and CDs cost $7 each. Satchi can spend no more than $35. a. Write an inequality that represents this situation. b. Does Satchi have enough money to buy 2 DVDs and 3 CDs?

10 12. FAMILY Tyrone said that the ages of his siblings are all part of the solution set of y > 2x, where x is the age of a sibling and y is Tyrone s age. Which of the following ages is possible for Tyrone and a sibling? Tyrone is 23; Maxine is 14. Tyrone is 18; Camille is 8. Tyrone is 12; Francis is 4. Tyrone is 11; Martin is 6. Tyrone is 19; Paul is FARMING The average value of U.S. farm cropland has steadily increased in recent years. In 2000, the average value was $1490 per acre. Since then, the value has increased at least an average of $77 per acre per year. Write an inequality to show land values above the average for farmland. 14. SHIPPING An international shipping company has established size limits for packages with all their services. The total of the length of the longest side and the girth (distance completely around the package at its widest point perpendicular to the length) must be less than or equal to 419 centimeters. Write and graph an inequality that represents this situation. 15. FUNDRAISING Troop 200 sold cider and donuts to raise money for charity. They sold small boxes of donut holes for $1.25 and cider for $2.50 a gallon. In order to cover their expenses, they needed to raise at least $100. Write and graph an inequality that represents this situation. 16. INCOME In 2006 the median yearly family income was about $48,200 per year. Suppose the average annual rate of change since then is $1240 per year. a. Write and graph an inequality for the annual family incomes y that are less than the median for x years after b. Determine whether each of the following points is part of the solution set. (2, 51,000) (8, 69,200) (5, 50,000) (10, 61,000)

11 Algebra 1 Section 4.4 Worksheet Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation. 1. (3, 2), y = x ( 2, 5), y = 4x (4, 6), y = 3 4 x (5, 4), y = 2 x 2 5. (12, 3), y = 4 x (3, 1), 2x + y = ( 3, 4), 3y = 2x 3 8. ( 1, 2), 3x y = 5 9. ( 8, 2), 5x 4y = ( 1, 4), 9x + 3y = ( 5, 6), 4x + 3y = (3, 1), 2x + 5y = 7 Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation. 13. ( 2, 2), y = 1 x ( 6, 5), x y = ( 4, 3), 4x + y = (0, 1), x + 5y = (2, 4), x 6y = ( 1, 7), 3x + 12y = ( 4, 1), 4x + 7y = (10, 5), 5x + 4y = (4, 5), 2x 5y = (1, 1), 3x + 2y = ( 6, 5), 4x + 3y = ( 3, 5), 5x 6y = GEOMETRY Quadrilateral ABCD has diagonals AC and. BD Determine whether AC is perpendicular to BD. Explain. 26. GEOMETRY Triangle ABC has vertices A(0, 4), B(1, 2), and C(4, 6). Determine whether triangle ABC is a right triangle. Explain. 27. BUSINESS Brady s Books is a retail store. The store s average daily profits y are given by the equation y = 2x + 3 where x is the number of hours available for customer purchases. Brady s adds an online shopping option. Write an equation in slope-intercept form to show a new profit line with the same profit rate containing the point (0, 12). 28. ARCHITECTURE The front view of a house is drawn on graph paper. The left side of the roof of the house is represented by the equation y = x. The rooflines intersect at a right angle and the peak of

12 the roof is represented by the point (5, 5). Write the equation in slope-intercept form for the line that creates the right side of the roof. 29. ARCHAEOLOGY An archaeologist is comparing the location of a jeweled box she just found to the location of a brick wall. The wall can be represented by the equation y = 5 x The box is located at the point (10, 9). Write an equation representing a line 3 that is perpendicular to the wall and that passes through the location of the box. 30. GEOMETRY A parallelogram is created by the intersections of the lines x = 2, x = 6, y = 1 x + 2, and another line. Find the 2 equation of the fourth line needed to complete the parallelogram. The line should pass through (2, 0). (Hint: Sketch a graph to help you see the lines.) 31. INTERIOR DESIGN Pamela is planning to install an island in her kitchen. She draws the shape she likes by connecting the vertices of the square tiles on her kitchen floor. She records the location of each corner in the table. Corner Distance from West Wall (tiles) Distance from South Wall (tiles) A 5 4 B 3 8 C 7 10 D 11 7 a. How many pairs of parallel sides are there in the shape ABCD she designed? Explain. b. How many pairs of perpendicular sides are there in the shape she designed? Explain. c. What is the shape of her new island?

13 Algebra 1 Section 4.7 Worksheet Find the inverse of each relation. 1. {( 2, 1), ( 5, 0), ( 8, 1), ( 11, 2)} 2. {(3, 5), (4, 8), (5, 11), (6, 14)} 3. {(5, 11), (1, 6), ( 3, 1), ( 7, 4)} 4. {(0, 3), (2, 3), (4, 3), (6, 3)} Graph the inverse of each function Find the inverse of each function. 8. f (x) = 6 4x + 2 x 3 9. f (x) = f (x) = 3x f (x) = 3(3x + 4) 12. f (x) = 5( x 6) 13. f (x) = 2x 3 7 Write the inverse of each equation in f 1 (x) notation x + 6y = y + 5x = x + 5y = x + 8y = y 3x = y 18. 2x 3 = 4x + 5y 19. CHARITY Jenny is running in a charity event. One donor is paying an initial amount of $20.00 plus an extra $5.00 for every mile that Jenny runs. a. Write a function D(x) for the total donation for x miles run. b. Find the inverse function, D 1 (x). c. What do x and D 1 (x) represent in the context of the inverse function? 20. BUSINESS Alisha started a baking business. She spent $36 initially on supplies and can make 5 dozen brownies at a cost of $12. She charges her customers $10 per dozen brownies.

14 a. Write a function C(x) to represent Alisha s total cost per dozen brownies. b. Write a function E(x) to represent Alisha s earnings per dozen brownies sold. c. Find P(x) = E(x) C(x). What does P(x) represent? d. Find C 1 (x), E 1 (x), and P 1 (x). e. How many dozen brownies does Alisha need to sell in order to make a profit? 21. GEOMETRY The area of the base of a cylindrical water tank is 66 square feet. The volume of water in the tank is dependent on the height of the water h and is represented by the function V(h) = 66h. Find V 1 (h). What will the height of the water be when the volume reaches 2310 cubic feet? 22. SERVICE A technician is working on a furnace. He is paid $150 per visit plus $70 for every hour he works on the furnace. a. Write a function C(x) to represent the total charge for every hour of work. b. Find the inverse function, C 1 (x). c. How long did the technician work on the furnace if the total charge was $640? 23. FLOORING Kara is having baseboard installed in her basement. The total cost C(x) in dollars is given by C(x) = x, where x is the number of pieces of wood required for the installation. a. Find the inverse function C 1 (x). b. If the total cost was $269 and each piece of wood was 12 feet long, how many total feet of wood were used? 24. BOWLING Libby s family went bowling during a holiday special. The special cost $40 for pizza, bowling shoes, and unlimited drinks. Each game cost $2. How many games did Libby bowl if the total cost was $112 and the six family members bowled an equal number of games?

15 Algebra 1 Section 5.3 Worksheet Justify each indicated step t (k + 8) 7 23 t a.? 5k a.? t 12 5k t 4 ( 12) 4 3 b.? 5k b.? t 16 5k 10 5k k 2 Solve each inequality. Check your solution. 3. 2b + 4 > x d a 4 < 2 7. t + 7 > j f + 3 < p + 5 3p k + 15 > 2k ( 3m 5) (w + 1) < 2(w + 5) 14. 2(q 3) Define a variable, write an inequality, and solve each problem. Check your solution. 15. Four more than the quotient of a number and three is at least nine. 16. The sum of a number and fourteen is less than or equal to three times the number. 17. Negative three times a number increased by seven is less than negative eleven. 18. Five times a number decreased by eight is at most ten more than twice the number. 19. Seven more than five sixths of a number is more than negative three. 20. Four times the sum of a number and two increased by three is at least twenty-seven. 21. BEACHCOMBING Jay has lost his mother s favorite necklace, so he will rent a metal detector to try to find it. A rental company charges a one-time rental fee of $15 plus $2 per hour to rent a metal detector. Jay has only $35 to spend. What is the maximum amount of time he can rent the metal detector?

16 22. AGES Bobby, Billy, and Barry Smith are each one year apart in age. The sum of their ages is greater than the age of their father, who is 60. How old can the oldest brother can be? 23. TAXI FARE Jamal works in a city and sometimes takes a taxi to work. The taxicabs charge $1.50 for the first 1 mile and $ for each additional 1 mile. Jamal has only $3.75 in his pocket. What is the maximum distance he can travel by taxi if he does not tip 5 the driver? 24. PLAYGROUND The perimeter of a rectangular playground must be no greater than 120 meters, because that is the total length of the materials available for the border. The width of the playground cannot exceed 22 meters. What are the possible lengths of the playground? 25. MEDICINE Clark s Rule is a formula used to determine pediatric dosages of over-the-counter medicines. weight of child ( lb) 150 adult dose = child dose a. If an adult dose of acetaminophen is 1000 milligrams and a child weighs no more than 90 pounds, what is the recommended child s dose? b. This label appears on a child s cold medicine. What is the adult minimum dosage in milliliters? Weight (lb) Age (yr) Dose under 48 under 6 call a doctor tsp or 10 ml c. What is the maximum adult dosage in milliliters?

17 Algebra 1 Section 5.5 Worksheet Match each open sentence with the graph of its solution set. 1. x 3 1 a. 2. 2x + 1 < 5 b x 3 c. Express each statement using an inequality involving absolute value. 4. The height of the plant must be within 2 inches of the standard 13-inch show size. 5. The majority of grades in Sean s English class are within 4 points of 85. Solve each inequality. Then graph the solution set. 6. 2z r > t + 6 < g 5 9 Write an open sentence involving absolute value for each graph RESTAURANTS The menu at Jeanne s favorite restaurant states that the roasted chicken with vegetables entree typically contains 480 Calories. Based on the size of the chicken, the actual number of Calories in the entree can vary by as many as 40 Calories from this amount. a. Write an absolute value inequality to represent the situation. b. What is the range of the number of Calories in the chicken entree? 15. SPEEDOMETERS The government requires speedometers on cars sold in the United States to be accurate within ±2.5% of the actual speed of the car. If your speedometer reads 60 miles per hour while you are driving on a highway, what is the range of possible actual speeds at which your car could be traveling?

18 16. BAKING Pete is making muffins for a bake sale. Before he starts baking, he goes online to research different muffin recipes. The recipes that he finds all specify baking temperatures between 350 F and 400 F, inclusive. Write an absolute value inequality to represent the possible temperatures t called for in the muffin recipes Pete is researching. 17. ARCHERY In an Olympic archery event, the center of the target is set exactly 130 centimeters off the ground. To get the highest score of ten points, an archer must shoot an arrow no further than 3.05 centimeters from the exact center of the target. a. Write an absolute value inequality to represent the possible distances d from the ground an archer can hit the target and still score ten points. b. Graph the solution set of the inequality you wrote in part a. 18. CATS During a recent visit to the veterinarian s office, Mrs. Van Allen was informed that a healthy weight for her cat is approximately 10 pounds, plus or minus one pound. Write an absolute value inequality that represents unhealthy weights w for her cat. 19. STATISTICS The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the individual scores deviate from the mean. For example, in a recent year the mean score on the mathematics section of the SAT test was 515 and the standard deviation was 114. This means that people within one deviation of the mean have SAT math scores that are no more than 114 points higher or 114 points lower than the mean. a. Write an absolute value inequality to find the range of SAT mathematics test scores within one standard deviation of the mean. b. What is the range of SAT mathematics test scores ±2 standard deviation from the mean?