Answers (Lesson 5-1) - Merrimack High School
Glencoe/McGraw-Hillriseruny 2yx2 2 x 15 }}22 2 54 2 (23)275 }7y 2 2 y1m5}x2 2 x1A222(27) 5 7(4 2 r)14 5 28 2 7r214 5 27r25r42r22} 5 }73 2 1042r22} 5 }727y2 2 y 1m5}x2 2 x 12slope of 2 } .7Divide each side by 27.Subtract 28 from each side.Distributive PropertyCross multiply.Simplify.2m 5 2}7 , y2 5 4, y1 5 r, x2 5 3, x1 5 10Slope formulaExample 2 Find the value of r so thatthe line through (10, r) and (3, 4) has a459. (4, 3.5), (24, 3.5) 08. (2, 5), (6, 2) 2 }346. (4, 23), (8, 23) 0undefined3. (24, 21), (24, 25)5. (14, 28), (7, 26) 2 }272. (24, 21), (22, 25) 22 Glencoe/McGraw-Hill10281216. (10, r), (3, 4), m 5 2 }7217. (10, 4), (22, r), m 5 20.513. (7, 25), (6, r), m 5 0 252Glencoe Algebra 1118. (r, 3), (7, r), m 5 2 }52315. (7, 5), (r, 9), m 5 6 }3314. (r, 4), (7, 1), m 5 }41112. (2, 8), (r, 24) m 5 23 6311. (21, 23), (7, r), m 5 }3410. (6, 8), (r, 22), m 5 1 24Determine the value of r so the line that passes through each pair of points hasthe given slope.7. (1, 22), (6, 2) }4. (2, 1), (8, 9) }431. (4, 9), (1, 6) 1Find the slope of the line that passes through each pair of points.ExercisesSimplify.y2 5 22, y1 5 5, x2 5 4, x1 5 23Slope formulaLet (23, 5) 5 (x1, y1) and(4, 22) 5 (x2, y2).Example 1 Find the slope of theline that passes through (23, 5)and (4, 22).of any two points on a nonvertical line21m 5 } or m 5 }, where (x1, y1) and (x2, y2) are the coordinatesSlopeSlope of a Line5 21PERIODStudy Guide and InterventionFind Slope5-1NAME DATE1.24 2 0.932000 2 197519501.241.481975 2000 2025*Year*Estimated0.93Source: United Nations Population Division00.51.0 0.551.52.0 20007480Source: USA TODAYWomenMen657075808590951008187*Estimated2025* 2050*Year Born7884Predicting Life ExpectancyGlencoe/McGraw-Hill282Glencoe Algebra 1decrease in rate from 2000–2025 to 2025–2050 is 0.04/yr. If the decreasein the rate remains the same, the change of rate for 2050–2075 might be0.08/yr and 25(0.08) 5 2 years of increase over the 25-year span.5. Make a prediction for the life expectancy for 2050–2075. Explain how you arrived atyour prediction. Sample answer: 89 for women and 83 for men; theincreases, it does not increase at aconstant rate.4. What pattern do you see in the increase with each25-year period? While life expectancylife expectancy at the same rates.3. Explain the meaning of your results in Exercises 1and 2. Both men and women increased their2. Find the rates of change for men from 2000–2025 and2025–2050. 0.16/yr, 0.12/yr1. Find the rates of change for women from 2000–2025and 2025–2050. 0.16/yr, 0.12/yrLONGEVITY The graph shows the predicted lifeexpectancy for men and women born in a given year.Exercisesc. How are the different rates of change shown on the graph?There is a greater vertical change for 1950–1975 than for 1975–2000. Therefore, thesection of the graph for 1950–1975 has a steeper slope.b. Explain the meaning of the slope in each case.From 1950–1975, the growth was 0.0152 billion per year, or 15.2 million per year.From 1975–2000, the growth was 0.0124 billion per year, or 12.4 million per year.5 } or 0.01240.31251975–2000: }}} 5 }}change in populationchange in time5 } or 0.01520.3825change in population0.93 2 0.551950–1975: }}} 5 }}change in time1975 2 1950Population Growth in ChinaPOPULATION The graph shows the population growth in China.a. Find the rates of change for 1950–1975 and for1975–2000.ExampleThe rate of change tells, on average, how a quantity is changing overtime. Slope describes a rate of change.Slope(continued)PERIODStudy Guide and InterventionRate of Change5-1NAME DATEPeople (billions) AgeAnswers(Lesson 5-1)Glencoe Algebra 1Lesson 5-1
SlopeSkills PracticeGlencoe/McGraw-Hillx23(1, –2)(0, 1)A3110SlopePractice(Average)0151 23 321415. } , } , 2 } , } }1 37 34 2 113. (12, 10), (12, 5) undefined11. (3, 9), (22, 8) }Oyx76 Glencoe/McGraw-Hill28325. (7, r), (4, 6), m 5 0 624. (5, 3), (r, 25), m 5 4 33423. (r, 4), (7, 1), m 5 } 1122. (r, 2), (6, 3), m 5 } 412Glencoe Algebra 1Glencoe Algebra 1Glencoe/McGraw-HillAnswers 284Glencoe Algebra 125. SALES A daily newspaper had 12,125 subscribers when it began publication. Five yearslater it had 10,100 subscribers. What is the average yearly rate of change in the numberof subscribers for the five-year period? 2405 subscribers per year2}324. ROOFING The pitch of a roof is the number of feet the roof rises for each 12 feethorizontally. If a roof has a pitch of 8, what is its slope expressed as a positive number?20. (r, 3), (5, 9), m 5 2 221. (5, 9), (r, 23), m 5 24 823. (r, 2), (5, r), m 5 0 21522. (r, 7), (11, 8), m 5 2 } 16Find the value of r so the line that passes through each pair of points has thegiven slope.19. (25, r), (1, 3), m 5 } 2418. (23, 24), (25, r), m 5 2 } 5921417. (24, 3), (r, 5), m 5 } 416. (22, r), (6, 7), m 5 } 312Find the value of r so the line that passes through each pair of points has thegiven slope.14. (0.2, 20.9), (0.5, 20.9) 013912. (22, 25), (7, 8) }1710. (15, 2), (26, 5) 2 }9. (5, 9), (3, 9) 0x(–2, 3)8. (27, 8), (27, 5) undefined4}5(–2, –3)(3, 1)3.7. (7, 24), (4, 8) 24xOy6. (6, 22), (5, 24) 2O2.5. (29, 23), (27, 25) 2123(–1, 0)(–2, 3)y4. (6, 3), (7, 24) 271.(3, 3)PERIODFind the slope of the line that passes through each pair of points.5-1NAME DATE21. (27, 2), (28, r), m 5 25 7719. (25, 6), (7, 28) 2 }6518. (24, 5), (28, 25) }2Lesson 5-120. (1, 4), (r, 5), m undefined 117. (12, 6), (3, 25) }7216. (5, 29), (3, 22) 2 }11915. (2, 21), (28, 22) }14. (10, 0), (22, 4) 2 }1313. (26, 24), (4, 1) }1211. (23, 10), (23, 7) undefined12. (17, 18), (18, 17) 2110. (25, 28), (28, 1) 239. (9, 8), (7, 28) 8(0, 0)Oy8. (2, 5), (23, 25) 21}3O(3, 1)3.7. (5, 2), (5, 22) undefinedxy6. (4, 6), (4, 8) undefined(2, 5)2.5. (6, 1), (26, 1) 02(0, 1)Oy4. (2, 5), (3, 6) 11.xPERIODFind the slope of the line that passes through each pair of points.5-1NAME DATEAnswers(Lesson 5-1)
Glencoe/McGraw-Hill3units, and the run isA4The graph is a vertical l285Glencoe Algebra 1Sample answer: If the slope is negative, choose the second pointso that its x-coordinate is less than that of the first point.3. The word rise is usually associated with going up. Sometimes going from one point onthe graph does not involve a rise and a run but a fall and a run. Describe how you couldselect points so that it is always a rise from the first point to the second point.slope used as rate of changerunSketchhow far up or down as compared to how far left or right 52,000 increase in spendingc. }}}}26 monthsb. }riserun21difference of y-coordinates divided by difference ofa. }corresponding x-coordinates2. Describe how each expression is related to slope.The graph is a horizontal line.y 2yx2 2 x1units.The graph falls as you go from left toright.Helping You Remember Description of Graph5The graph rises as you go from left toright.zeronegativepositiveType of Slope1. Describe each type of slope and include a sketch.Reading the Lesson3 units3Thus, the slope of this line is } or } .5 units5In this graph, the rise isslope 5 }riserunRead the introduction to Lesson 5-1 at the top of page 256 in yourtextbook. Then complete the definition of slope and fill in the boxeson the graph with the words rise and run.Why is slope important in architecture?SlopeyPERIODReading to Learn MathematicsPre-Activity5-1NAME DATEEnrichment Glencoe/McGraw-Hill329. }5. 11. 3Start Here1310. }6. 21142. }2863411. 2 }7. no slope253. 2 }12. 3278. }4. 0TreasureGlencoe Algebra 1PERIODUsing the definition of slope, draw lines with the slopes listedbelow. A correct solution will trace the route to the treasure.Treasure Hunt with Slopes5-1NAME DATEAnswers(Lesson 5-1)Glencoe Algebra 1Lesson 5-1
Glencoe/McGraw-HillSlope and Direct VariationStudy Guide and Intervention1O(0, 0)(2, 1)x111A5Simplify.(x1, y1) 5 (0, 0), (x2, y2) 5 (2, 1)Slope formulab. Use the direct variation equation tofind x when y 5 18.y 5 6xDirect variation equation18 5 6xReplace y with 18.35xDivide each side by 6.Therefore, x 5 3 when y 5 18.a. Write a direct variation equationthat relates x and y.Find the value of k.Direct variation equationy 5 kx30 5 k(5)Replace y with 30 and x with 5.65kDivide each side by 5.Therefore, the equation is y 5 6x.Suppose y variesdirectly as x, and y 5 30 when x 5 5.Example 2O22; 22(–1, 2)(0, 0)yy 5 –2xx2.3; 3O(1, 3)(0, 0)yy 5 3xx3.3 3}; }2 2(–2, –3)(0, 0)Oyxy 5 32 x Glencoe/McGraw-Hill28732y 5 2x; 325. If y 5 9 when x 5 23, find x when y 5 6. y 5 23x; 226. If y 5 24.8 when x 5 21.6, find x when y 5 224. y 5 3x; 2831137. If y 5 }when x 5 }, find x when y 5 }. y 5 2x; }48164. If y 5 4 when x 5 2, find y when x 5 16.Glencoe Algebra 1Write a direct variation equation that relates x to y. Assume that y varies directlyas x. Then solve.1.Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.ExercisesThe slope is }.215}21205}220221m5}x 2xy 2yFor y 5 }x, the constant of variation is }.22y 5 12 xyName the constant ofvariation for the equation. Then findthe slope of the line that passesthrough the pair of points.Example 1A direct variation is described by an equation of the form y 5 kx,where k Þ 0. We say that y varies directly as x. In the equation y 5 kx, k is the constantof variation.Direct Variation5-2PERIODTRAVEL A family drove their car 225 miles in 5 hours.rise}run1Glencoe Algebra 1Glencoe/McGraw-HillAnswers 5 ft32886. Find the volume of the same gas at 250 (absolute temperature).5. Graph the equation on the grid at the right.4. Write a direct variation equation that relates the variables.V 5 0.02Tpressure, volume of a gas V varies directly as its temperatureT. A volume of 4 cubic feet of a certain gas has a temperatureof 200 (absolute temperature).CHEMISTRY Charles’s Law states that, at a constant33. Find the cost of }4 pound of jelly beans. 3.372. Graph the equation on the grid at the right.C 5 4.49p0901802701. Write a direct variation equation that relates the variables.RETAIL The total cost C of bulk jelly beans is 4.49 times the number of pounds p.ExercisesTherefore, it will take 8 hours to drive 360 miles. CHECK (5, 225) lies on the graph.c. Estimate how many hours it would take thefamily to drive 360 miles.d 5 45tOriginal equation360 5 45tReplace d with 360.t58Divide each side by 45.m5 }4518tV0123404.509.0013.5018.00CGlencoe Algebra 1100200TTemperature (8K)Charles’s Laww24Weight (pounds)Cost of Jelly Beans7(5, 225)(1, 45)2 3 4 5 6Time (hours)d 5 45ta. Write a direct variation equation to find the distance traveled for any numberof hours.Use given values for d and t to find r.d 5 rtOriginal equation225 5 r(5) d 5 225 and t 5 545 5 rDivide each side by 5.Therefore, the direct variation equation is d 5 45t.b. Graph the equation.Automobile TripsThe graph of d 5 45t passes through the origin withdslope 45.360ExampleThe distance formula d 5 rt is a direct variation equation. In theformula, distance d varies directly as time t, and the rate r is the constant of variation.Slope and Direct Variation(continued)PERIODStudy Guide and InterventionSolve Problems5-2NAME DATEDistance (miles)NAME DATECost (dollars) Volume (cubic feet)Answers(Lesson 5-2)Lesson 5-2
Slope and Direct VariationSkills PracticePERIODy 5 13 x(0, 0)Oy(3, 1)xOyy 5 –2x(–1, 2)O(0, 0)y35. y 5 2 } x42.xOyxOy 5 – 32 x(–2, 3)26. y 5 } x522; 22 3.(0, 0)yOyxy5}x ; 2243232}2 Glencoe/McGraw-HillC 5 1.80g46 8 10 12 14 gGallons289032640912151821T8T 5 3c123 4 5Crates7cGlencoe Algebra 16Toys Shipped14. SHIPPING The number of delivered toys Tis 3 times the total number of crates c.1216202428CGasoline Cost13. TRAVEL The total cost C of gasolineis 1.80 times the number of gallons g.x32};Write a direct variation equation that relates the variables. Then graph theequation.y5}x; }4212. If y 5 12 when x 5 18, find x2when y 5 216.10. If y 5 29 when x 5 3, find ywhen x 5 25. y 5 23x ; 159. If y 5 24 when x 5 2, find ywhen x 5 26. y 5 22x ; 1211. If y 5 4 when x 5 16, find y13when x 5 6.8. If y 5 45 when x 5 15, find xwhen y 5 15. y 5 3x ; 57. If y 5 28 when x 5 22, find xwhen y 5 32. y 5 4x ; 8Write a direct variation equation that relates x and y. Assume that y variesdirectly as x. Then solve.4. y 5 3xx1 1}; }3 3Graph each equation.1.Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.5-2NAME DATECost ( )A6ToysGlencoe/McGraw-Hill(Average)Slope and Direct VariationPracticePERIOD(0, 0)Oyy 5 34 xx(4, 3)3 3}; }4 4Oyx65(0, 0)Oy5. y 5 } x2.Oyxy 5 43 x(3, 4)x4 4}; }3 3(–2, 5)53O(0, 0)y 5 2 52 xy6. y 5 2 } x3.x348. If y 5 80 when x 5 32, find x when y 5 100.3280246810246 8 10 12 ,LengthRectangle DimensionsWC 5 4.50t0510152025C123 4 5Tickets6Cost of Tickets 12x2Glencoe/McGraw-Hill290to their weight. Then find the cost of 4 } pounds of bananas.14Glencoe Algebra 1C 5 0.32p ; 1.363 } pounds of bananas for 1.12. Write an equation that relates the cost of the bananast11. TICKETS The total cost C of tickets is 4.50 times the number of tickets t.12. PRODUCE The cost of bananas varies directly with their weight. Miguel bought32W5},10. MEASURE The width W of arectangle is two thirds of the length ,.Write a direct variation equation that relates the variables. Then graph theequation.9. If y 5 } when x 5 24, find y when x 5 12.y 5 15x; 24.5y 5 2.5x; 4031y5}x; }7. If y 5 7.5 when x 5 0.5, find y when x 5 20.3.Oy2552};2 }Write a direct variation equation that relates x and y. Assume that y variesdirectly as x. Then solve.4. y 5 22xGraph each equation.1.Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.5-2NAME DATEWidth Cost ( )Answers(Lesson 5-2)Glencoe Algebra 1Lesson 5-2
Glencoe/McGraw-HillA7Sample answer: For each minute the shower runs, 6 gallonsof water come out. So, if the shower ran 10 minutes, thatwould be 60 gallons. Think about the first sentence. What does it mean to say that a standardshowerhead uses about 6 gallons of water per minute?They are the coordinates of the points on the graph. How do the numbers in the table relate to the graph shown?Read the introduction to Lesson 5-2 at the top of page 264 in your textbook.How is slope related to your shower?Slope and Direct VariationGlencoe/McGraw-Hill291Glencoe Algebra 1of variation relates x and y in the same value every time, and thatrelationship never changes.5. Look up the word constant in a dictionary. How does this definition relate to the termconstant of variation? Sample answer: Something unchanging; the constantHelping You Rememberc. The wages W earned by an employee vary directly with the number of hours h thatare worked. Enrique earned 172.50 for 23 hours of work. W 5 7.50hb. The perimeter p of a pentagon with all sides of equal length varies directly as thelength s of a side of the pentagon. A pentagon has 5 sides. p 5 5sd 5 88ta. The distance d varies directly as time t, and a cheetah can travel 88 feet in 1 second.4. For each situation, write an equation with the proper constant of variation.3. The expression “y varies directly as x” can be written as the equation y 5 kx. How wouldyou write an equation for “w varies directly as the square of t”? w 5 kt 2the same value as the slope of the graph of the equation.2. How is the constant of variation related to slope? The constant of variation has1. What is the form of a direct variation equation? y 5 kxReading the Lesson PERIODReading to Learn MathematicsPre-Activity5-2NAME DATEEnrichmentPERIODGlencoe Algebra 17440 poundsGlencoe/McGraw-Hill292Glencoe Algebra 1Answers will vary. For example, bone strength limits the size humanscan attain.9. What can you conclude from Exercises 7 and 8?only 2224 pounds8. According to the adult equation for weight supported (Exercise 5), howmuch weight could a 20-foot tall giant’s legs actually support?Answers 37. According to the adult equation you found (Exercise 1), how muchwould an imaginary giant 20 feet tall weigh?5k 5 2.16 for h 5 }ft6. For a baby who is 20 inches long and weighs 6 pounds, find an “infantvalue” for k in the equation s 5 kh2.k 5 5.565. For a person 6 feet tall who weighs 200 pounds, find a value for k in theequation s 5 kh2.k has a greater value.4. How does your answer to Exercise 3 demonstrate that a baby issignificantly fatter in proportion to its height than an adult?35k 5 1.296 for h 5 }ft3. Find the value for k in the equation w 5 kh3 for a baby who is 20 incheslong and weighs 6 pounds.2. Use your answer from Exercise 1 to predict the weight of a person whois 5 feet tall. about 116 poundsk 5 0.931. For a person 6 feet tall who weighs 200 pounds, find a value for k in theequation w 5 kh3.Answer each question.The weight that a person’s legs will support is proportional to thecross-sectional area of the leg bones. This area varies directly as the squareof the person’s height. The equation of variation has the form s 5 kh2.Assume that the weight of a person of average build varies directly as thecube of that person’s height. The equation of variation has the formw 5 kh3.An equation of the form y 5 kxn, where k Þ 0, describes an nth powervariation. The variable n can be replaced by 2 to indicate the second powerof x (the square of x) or by 3 to indicate the third power of x (the cube of x).nth Power Variation5-2NAME DATEAnswers(Lesson 5-2)Lesson 5-2
PERIODSlope-Intercept FormStudy Guide and Interventiony 5 mx 1 b, where m is the given slope and b is the y-intercept3Simplify.Divide each side by 24.Subtract 3x from each side.3O(0, –2)yx3x 2 4y 5 8(4, 1)A8y 5 22x 2 12. slope: 22, y-intercept 21(0, –2)(1, 0)y 5 2x 2 2Oyx Glencoe/McGraw-HillOy7. y 5 2x 1 1xGraph each equation.4.(3, 0)y 5 2x 1 3O(0, 3)yO293y8. y 5 23x 1 25.xxWrite an equation of the line shown in each graph.y 5 8x 2 31. slope: 8, y-intercept 23(0, –5)(4, –2)43y5 }x25OyOyxxGlencoe Algebra 19. y 5 2x 2 16.y 5 2x 2 73. slope: 21, y-intercept 27Write an equation of the line with the given slope and y-intercept.ExercisesThe y-intercept of y 5 }x 2 2 is 22 and the slope is }. So graph the point (0, 22). From44this point, move up 3 units and right 4 units. Draw a line passing through both points.24y23x 1 8} 5 }}24243y5}x224Original equationGraph 3x 2 4y 5 8.3x 2 4y 5 824y 5 23x 1 8Example 2Example 1 Write an equation of the line whose slope is 24 and whosey-intercept is 3.Slope-intercept formy 5 mx 1 by 5 24x 1 3Replace m with 24 and b with 3.Slope-Intercept FormSlope-Intercept Form5-3NAME DATESlope-Intercept Form1. Write an equation to find the percent P of households thatsubscribed to cable TV for any year x between 1995 and 1999. Glencoe/McGraw-Hill2946. Find the population in 2050. about 400,000,0005. Graph the equation on the grid at the right.4. Write an equation to find the population P in any year xbetween 2010 and 2050. P 52,500,000x 1 300,000,000projected to be 300 million by the year 2010. Between2010 and 2050, the population is expected to increase byabout 2.5 million per year.POPULATION The population of the United States is3. Find the percent that subscribed to cable TV in 1999. 68.1%2. Graph the equation on the grid at the right.P 5 0.6x 1 65.7010,50010,60010,70010,80010,900N12 3 4 5 6Years Since 1997Cable TV Systemsx1 2 3 4 5 xYears Since 1995Glencoe Algebra 10x2040Years Since 2010Source: The World Almanac300320340360380400PProjected UnitedStates PopulationSource: The World Almanac065666768PPercent of Householdswith TV Having CableSource: The World Almanacwith TV’s in the U.S. subscribed to cable TV. Between 1995and 1999, the percent increased by about 0.6% each year.ENTERTAINMENT In 1995, 65.7% of all householdsExercisesThere were about 10,580 cable TV systems in 2000.c. Find the approximate number of cable TVsystems in 2000.N 5 2121x 1 10,943Original equationN 5 2121(3) 1 10,943Replace x with 3.N 5 10,580Simplify.b. Graph the equation.The graph of N 5 2121x 1 10,943 is a line that passesthrough the point at (0, 10,943) and has a slope of 2121.a. Write a linear equation to find the average number of cable systems in any yearafter 1997.The rate of change is 2121 systems per year. In the first year, the number of systems was10,943. Let N 5 the number of cable TV systems. Let x 5 the number of years after 1997.An equation is N 5 2121x 1 10,943.ExampleMEDIA Since 1997, the number of cable TV systems has decreasedby an average rate of 121 systems per year. There were 10,943 systems in 1997.(continued)PERIODStudy Guide and InterventionModel Real-World Data5-3NAME DATENumber of Cable TV SystemsGlencoe/McGraw-HillPercent Population (millions)Answers(Lesson 5-3)Glencoe Algebra 1Lesson 5-3
Glencoe/McGraw-HillA9Slope-Intercept FormSkills PracticePERIOD(0, –3)(2, 1)y 5 2x 2 3OyxOyx(2, –4)xy 5 23x 1 2O(0, 2)yOy13. y 5 22x 2 110.xO(2, –3)Oyy 5 2x 2 1(0, –1)yy5814. x 1 y 5 2311.8. slope: 0, y-intercept: 8x Glencoe/McGraw-HillA 5 2500m 1 3000295Glencoe Algebra 118. An airplane at an altitude of 3000 feet descends at a rate of 500 feet per mile.W 5 22m 1 3017. A Cairn terrier weighs 30 pounds and is on a special diet to lose 2 pounds per month.H 5 1.5t 1 1.516. A Norfolk pine is 18 inches tall and grows at a rate of 1.5 feet per year.C 5 2r 1 1015. A video store charges 10 for a rental card plus 2 per rental.xy 5 24x 2 9Write a linear equation in slope-intercept form to model each situation.12. y 5 x 1 4Graph each equation.9.y 5 22x 1 76. slope: 24, y-intercept: 29Write an equation of the line shown in each graph.y 5 x 2 12y 5 3x 1 27. slope: 1, y-intercept: 2125. slope: 3, y-intercept: 22. slope: 22, y-intercept: 7y 5 26x 2 2 4. slope: 7, y-intercept: 1 y 5 7x 1 1y 5 5x 2 33. slope: 26, y-intercept: 221. slope: 5, y-intercept: 23Write an equation of the line with the given slope and y-intercept.5-3NAME DATE(Average)Slope-Intercept FormPractice145O2y5}x12(–5, 0)(0, 2)yxx2O(0, 3)3y5}x13(–2, 0)yOy9. 3y 5 2x 2 66.xxOy10. 6x 1 3y 5 63x2y 5 2}x22(0, –2)(–3, 0)Oy2Glencoe Algebra 1Glencoe/McGraw-HillAnswers 29615. Find the total number of pages written after 5 months. 8514. Graph the equation on the grid at the right.13. Write an equation to find the total number of pages Pwritten after any number of months m. P 5 10 1 15mWRITING For Exercises 13–15, use the following information.Carla has already written 10 pages of a novel. She plansto write 15 additional pages per month until she is finished.P 5 27t 1 6791020406080100PxC 5 35h 1 75126 mGlencoe Algebra 13 4 5MonthsCarla’s Novel12. The population of Pine Bluff is 6791 and is decreasing at the rate of 7 per year.11. A computer technician charges 75 for a consultation plus 35 per hour.Write a linear equation in slope-intercept form to model each situation.Oy8. y 5 2 } x 1 212Graph each equation.5.7.y 5 22.5x 1 3.54. slope: 22.5, y-intercept: 3.5322. slope: } , y-intercept: 24Write an equation of the line shown in each graph.y 5 1.5x 2 141y5}x133. slope: 1.5, y-intercept: 211. slope: } , y-intercept: 33y5}x 24PERIODWrite an equation of the line with the given slope and y-intercept.5-3NAME DATEPages WrittenAnswers(Lesson 5-3)Lesson 5-3
Glencoe/McGraw-HillA10It is the slope. How does the rate of 0.10 per minute relate to the graph? What point on the graph shows that the flat fee is 5.00? (0, 5)Read the introduction to Lesson 5-3 at the top of page 272 in your textbook.How is a y-intercept related to a flat fee?Slope-Intercept Formy-interceptrate of growth0.2?0.63 weeks after birth 1 weight at birthGlencoe/McGraw-Hill297Glencoe Algebra 1rise-over-run definition of slope to determine how far up or down andright or left the next point is from the first.5. One way to remember something is to explain it to another person. Write how you wouldexplain to someone the process for using the y-intercept and slope to graph a linearequation. On the y-axis, plot the point for the y-intercept. Then use theHelping You Rememberc. Use the variables you defined and what you know from the problem to write anequation. W 5 0.2t 1 0.6W be the weight at any time and t be the number of weeks after birth.b. Define what variables to use for the unknown quantities. Sample answer: Letweight?5a. Write a verbal equation to show how the words are related to finding the averageweight of a ruby-throated hummingbird at any given week. Use the words weight atbirth, rate of growth, weight, and weeks after birth. Below the equation, fill in anyvalues you know and put a question mark under the items that you do not know.A ruby-throated hummingbird weighs about 0.6 gram at birth and gains weight at a rateof about 0.2 gram per day until fully grown.4. Read the problem. Then answer each part of the exercise.The slope is 0, and the y-intercept is where it crosses the y-axis.3. What are the slope and y-intercept of a horizontal line?The slope is undefined, and there is no y-intercept.2. What are the slope and y-intercept of a vertical line?slopey 5 mx 1 b 1. Fill in the boxes with the correct words to describe what m and b represent.Reading the Lesson PERIODReading to Learn MathematicsPre-Activity5-3NAME DATEEnrichmenty 2yx2 2 x1BB Glencoe/McGraw-Hill1m5 }, b 5 2327. x 2 2y 5 62m 5 2}, b 5 2635. 4x 1 6y 5 236m 5 22, b 5 243. 2x 1 y 5 24298m 5 0, b 5 58. 4y 5 2031m5 },b596. x 2 3y 5 22734m 5 2},b584. 4x 1 3y 5 24Use the expressions in Exercise 2 above to find the slope andy-intercept of each equation.BACm 5 2},b5 }2. Use the slope-intercept equation you wrote in Exercise 1 to writeexpressions for the slope and the y-intercept in terms of A, B, and C.BCAy 5 2}x1 }1. Solve Ax 1 By 5 C for y. Your answer should be written inslope-intercept form.Another definition can be found from the standard from of a linearequation. Standard form is Ax 1 By 5 C, where A, B, and C areintegers, A 0, and A and B are not both zero.riserun21You have learned that slope can be defined in terms of } or }.Glencoe Algebra 1PERIODRelating Slope-Intercept Form and Standard Forms5-3NAME DATEAnswers(Lesson 5-3)Glencoe Algebra 1Lesson 5-3
Writing Equations in Slope-Intercept FormGlencoe/McGraw-Hill1412Therefore, the equation is y 5 } x 2 } .141Add }to each side.12} 5 b22Multiply.121 5 2 } 1 b2Slope-intercept form1m5 }, y 5 21, and x 5 22421 5 } (22) 1 b14y 5 mx 1 bwith (22, 21) in the slope-intercept form.The line has slope } . Replace m with } and (x, y)14Example 2 Write an equation of the line1that passes through (22, 21) with slope } .A11m5234(3, 5)y 5 2x 2 1OyxOy 5 22xm 5 –2(0, 0)yx(2, 4)21y5}x13Om 5 12y12x9. (1, 24), m 5 26y 5 26x 1 28. (2, 2), m 5 }121y5}x11221y 5 2}x236. (4, 25), m 5 2 }3.y 5 5x 1 25. (21, 23), m 5 52. Glencoe/McGraw-Hill51y5}x 1 350299Glencoe Algebra 1112. Write an equation of a line that passes through the point (0, 350) with slope } .5y 5 23x 1 1211. Write an equation of a line that passes through the x-intercept 4 with slope 23.y 5 2x 2 310. Write an equation of a line that passes through the y-intercept 23 with slope 2.y547. (25, 4), m 5 043y 5 2}x184. (8, 2), m 5 2 }1.Write an equation of the line that passes through each point with the given slope.ExercisesThe line has slope 3. To find they-intercept, replace m with 3 and (x, y)with (24, 2) in the slope-intercept form.Then solve for b.Slope-intercept formy 5 mx 1 b2 5 3(24) 1 bm 5 3, y 5 2, and x 5 242 5 212 1 bMultiply.14 5 bAdd 12 to each side.Therefore, the equation is y 5 3x 1 14.Example 1 Write an equation ofa line that passes through (24, 2)with slope 3.4PERIODStudy Guide and InterventionWrite an Equation Given the Slope and One Point5-4NAME DATEWriting Equations in Slope-Intercept Form(continued)PERIODStudy Guide and InterventionWrite an equation of the line that passes through (1, 2) and (3, 22).(0, –3)(1, 1)y 5 4x 2 3Oyx(4, 0)y 5 2x 14Oy(0, 4)2x1y 5 2}x148. (10, 21), (4, 2)y 5 5x 1 25. (0, 2), (1, 7)2.(0, 1)31y5 }x11(–3, 0) Oyx73y5 }x149. (214, 22), (7, 7)y 5 24x 2 16. (6, 225), (21, 3)3.Glencoe Algebra 1Glencoe/McGraw-HillAnswers 58y5 }x 1 1630012. Write an equation of a line that passes through (0, 16) and (210, 0).35y5 }x15Glencoe Algebra 111. Write an equation of a line that passes through the x-intercept 23 and y-intercept 5.21y5 }x2210. Write an equation of a line that passes through the x-intercept 4 and y-intercept 22.y 5 3x 1 57. (22, 21), (2, 11)y 5 22x 1 44. (21, 6), (7, 210)1.Write an equation of the line that passes through each pair of points.Exercisesy 5 mx 1 bSlope-intercept form2 5 22(1) 1 bReplace m with 22, y with 2, and x with 1.2 5 22 1 bMultiply.45bAdd 2 to each side.Therefore, the equation is y 5 22x 1 4.m 5 22Simplify.y2 5 22, y1 5 2, x2 5 3, x1 5 1m5 }22 2 23 21Slope formula21m5}x2 2 x1y 2yFind the slope m. To find the y-intercept, replace m with its computed value and (x, y) with(1, 2) in the slope-intercept form. Then solve for b.ExampleWrite an Equation Given Two Points5-4NAME DATEAnswers(Lesson 5-4)Lesson 5-4
Writing Equations in Slope-Intercept FormSkills PracticePERIODGlencoe/McGraw-HillOxy 5 23x 1 1m 5 –3(–1, 4)ym51(4, 1)y5x23Oyy 5 2x 1 4Oy 5 2x 1 4m52(–1, 2)yA12(–1, –3)O(1, 1)x Glencoe/McGraw-Hilly 5 22x 2 823. x-intercept: 24, y-intercept: 28y 5 22x 1 221. x-interc
Glencoe/McGraw-Hill A5 Glencoe Algebra 1 Answers NAME _ DA Study Guide and Intervention Slope and Direct Variation TE _ PERIOD _ 5-2 Glencoe/McGraw-Hill
4 Step Phonics Quiz Scores Step 1 Step 2 Step 3 Step 4 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 . Zoo zoo Zoo zoo Yoyo yoyo Yoyo yoyo You you You you
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Lesson 41 Day 1 - Draft LESSON 42 - DESCRIPTIVE PARAGRAPH Lesson 42 Day 1 - Revise Lesson 42 Day 1 - Final Draft Lesson 42 - Extra Practice LESSON 43 - EXPOSITORY PARAGRAPH Lesson 43 Day 1 - Brainstorm Lesson 43 Day 1 - Organize Lesson 43 Day 1 - Draft LESSON 44 - EXPOSITORY PARAGRAPH Lesson 44 Day 1 - Revise
