Assignment 5.9 Different Representations of a Linear Relation
1) Use each of the linear relations below to determine the rate. Show your work. a)
Number of Subscriptions
Sold, 𝒏
Total Daily Pay ($) 0 20 1 28 2 36 3 44 4 52 b)
Week, 𝒘 Amount Still
Owing, 𝑨, ($) 0 100 1 95 2 90 3 85 4 80 5 75 c) Number of Hours, 𝒏 Rental Cost, 𝑪, ($) 0 10 1 13 2 16 3 19 d) Number of Movies, 𝒏 Total Cost, 𝑪, ($) 1 12 2 14 3 16 4 18 e) Number of Toppings, 𝒏 Rental Cost, 𝑪, ($) 0 3 2 7 4 11 6 15 f) Number of games, 𝒏 Total Cost, 𝑪, ($) 3 51 5 85 9 153 12 204 g) Number of Songs, 𝒏 Total Monthly Cost, 𝑪, ($) 10 8.00 20 13.00 30 18.00 40 23.00 h) Number of People, 𝒏 Total Cost, 𝑪, ($) 10 275 20 450 30 625 i) Number of Rides, 𝒏 Total Cost, 𝑪, ($) 3 12 9 14 21 18 j) Number of Trees Sold, 𝒏 Total Amount Raised, 𝑨, ($) 3 240 9 420 11 480 k) Repair Time, 𝒕, (hr) Cost, 𝑪, ($) 3 205 6 385 8 505 l) Number of Classes, 𝒏 Total Cost, 𝑪, ($) 12 67 14 74 16 81
2) Write the equation for each of the following linear relations.
a) b) c)
d) e) f)
3) The total cost of a banquet includes a fixed fee to rent the hall and a cost per person. Information about the total cost at two different halls is shown below. Which hall’s total cost includes a lower cost per person?
Hall A: Number of People, 𝒏 Total Amount Raised, 𝑨, ($) 10 275 20 450 30 625 Hall B:
4) Water is leaking from a bottle at a constant rate. Julia draws the line on the graph below to model the relationship between the volume of water remaining and time.
a) Determine the rate at which the water is leaking. b) Determine the equation that models this relationship. c) Determine whether each of the 3 points shown on the line is possible in this situation. Write an interpretation of the meaning of each point.
5) The total cost to print posters includes a set-up fee plus a charge per poster. The graph below represents the relationship between C, the total cost, and n, the number of posters printed. a) Determine the equation that represents the cost to print a poster. What do your variables represent?
b) Determine the cost to print 96 posters. Show your work. c) Jacob paid $210 to print posters for his band. How many posters did he print? Show your work.
Answers Assignment 5.9: Different Representation of Linear Relations
1) a) $8/subscription b) $5/week c) $3/hour d) $2/movie e) $2/topping f) $17/game e) $0.50/song h) $17.50/person i) $2/ride
j) $60/tree k) $60/h l) $3.50/class
2) a) $–15/min, $100 initially, 𝐶 = −15𝑚 + 10 b) $0.50/ride, $3 initially, 𝐶 = 0.50𝑚 + 3 c) $0.50/km, $20 initially, 𝐶 = 0.50𝑚 + 20 d) $0.05/message, $10 initially, 𝐶 = 0.05𝑚 + 10 e) $2.50/game, $5 initially, 𝐶 = 2.5𝑔 + 5 f) –100m/mi, 500m initially,
𝐻 = −100𝑚 + 500 g) $5/t-shirt, $75 initially, 𝐶 = 5𝑡 + 75 h) $1.50/poster, $15 initially, 𝐶 = 1.50𝑝 + 15 i)$–2000/year, $20 000 initially, 𝑉 = −2000𝑦 + 20 000 3) Hall A would cost $17.50 per person, Hall B would cost $15 per person, Hall B would be cheaper.
4) a) -150ml/min b) C = -150t + 500 c) Point A is possible, it the initial value. There is 500 ml in the bottle at the start, Point B is
possible, after 2 minutes there 200 ml in the water bottle. Point C is impossible, you can’t have a negative amount of water in a water bottle. 5) a) 𝐶 = 15 + 0.15𝑝 b) $159 c) 130 posters
Assignment 5.10: Partial vs. Direct Variation and Changing Conditions
1) For each of the following relations, determine the initial value, type of variation, rate of change, and the equation of the graph.
a) A florist charges $20 for a vase, plus $2 per flower.
b) A mechanic charges $50 per hour, plus a $200 for parts.
c) d)
f)
Number Sold, 𝒏 Money
Earned, M, ($) 0 35 4 55 8 75 12 95 g) Temperature, T, (°𝑪) Radius of Snowball, R, (𝒄𝒎) – 6 38 – 3 32 0 26 3 20
2) The following graph show’s Alice’s expenses for running her sandwich making business.
a) Determine the initial value of the graph? What does it represent?
b) Determine the rate of change of the graph? What does it represent?
c) Write the equation of this graph where M is the money earned and n is the number of sandwiches made.
d) Does this relationship represent partial or direct? Explain how you know.
3) The following graph shows the cost of hiring Paula the Plumber.
a) What is the initial value of the graph? b) What does the initial value represent? c) Calculate the rate of change?
d) What does the rate of change represent? e) Write the equation for this graph.
f) How much would it cost to hire her for a job that took 15 hours? Use the equation and show your work.
g) How many hours would it take to earn $1125? Use the equation and show your work.
4) Each month, Alex’s cellphone plan costs $15, plus $0.10 per minute of use. a) Describe why the following two graphs cannot represent Alex’s cellphone plan. b) Sketch a graph that could represent Alex’s cellphone plan. Explain why your graph is correct.
c) Create an equation that represents the cost of Alex’s cellphone plan. What do your variables represent?
d) Use your equation to determine the cost of 100 minutes. Show your work. e) Use your equation to determine how many minutes Alex could talk for $40. Show your work.
5) The total cost at an amusement park is made up of an admission fee and a cost per ride. Information about the total cost for n rides last year is shown below.
a) Determine the initial value and rate for the relationship. Show your work.
b) Write an equation for the cost at amusement park last year. c) This year, the admission fee increases to $20, but the cost per ride remained the same. Write an equation for the cost at amusement park last year. Then draw this year’s line.
6) The total cost of renting a car on weekdays is represented by the graph. On weekends, the flat fee remains the same but the cost per kilometre is less. Decide if each statement is true or false.
a) The weekend graph goes through the point (0, 0).
b) The weekend graph stays the same as the weekday graph. c) The initial cost is the same for both graphs.
d) The weekend graph is steeper than the weekday graph. e) The weekend graph is less steep than the weekday graph. f) The weekend graph will start lower than the weekday graph. g) The weekend graph will start higher than the weekday graph.
7. A local fair charges a $15 entry fee and $1.75 per ride. Dustin has $35 to spend. What is the maximum number of rides Dustin can go on? Justify your answer.
8. Water is being pumped to empty a swimming pool. At 6 a.m., the water level is 150 cm. Every 2 hours, the water level drops by 30 cm. What is the earliest time when the pool will be empty?
9. The equations below represent the relationship between the total cost, 𝐶, in dollars, to repair a computer and the amount of time, 𝑡, in hours, at two computer repair stores.
Compu-Fix 𝐶 = 10 + 15𝑡
Data Repair 𝐶 = 30 + 12𝑡
It will take between 1 and 5 hours to repair Maria’s computer. What are the smallest and largest possible amounts Maria could pay? Justify your answer.
10. A catering company charges according to the equation 𝐶 = 46𝑛 + 385 , where 𝐶 represents the total cost, in dollars, and 𝑛 represents the number of plates served. Cameron would like to use this catering company for his next event. He finds out that the catering company requires a minimum of 25 plates, but does not want to go over his budget of $3000. What are the possible values of 𝐶 and 𝑛 in this situation? Justify your answer. 11. Working as an insurance salesperson, Ilya earns a base salary of $520 and a commission of $80 on each new policy.
a) Write an equation to represent this situation, with 𝐸 representing Ilya’s earnings in dollars, and 𝑛 representing the number of new policies he sells during the week
b) If Ilya has the potential to sell a maximum of 15 policies each week, what are the possible amounts that he could earn? Justify your answers.
Answers Assignment 5.10: Partial vs. Direct Variation and Changing Conditions
1) a) IV = $20; Partial Variation; ROC = $2 per flower; 𝐶 = 20 + 2𝐹 b) IV = $200; Partial Variation; ROC = $50 per hour; 𝐶 = 200 + 20𝑛
c) IV = $0; Direct Variation; ROC = $20 per hour; 𝐶 = 0 + 20𝑛 d) IV = $100; Partial Variation; ROC = $–12 per hour; 𝑀 = 100 − 12ℎ e) IV = $35; Partial Variation; ROC = $5 per hour; 𝑀 = 35 + 5𝑛 f) IV = 26 cm; Partial Variation; ROC = -2 cm per hour; 𝑅 = 26 − 2𝑇
2) a) $20. This is her initial cost for things like rent and electricity. b) $1.50 per sandwich. This is the cost of making each sandwich.
c) 𝑀 = 20 + 1.50𝑛 d) Partial – Her expenses have an initial value
3) a) $75 b) The cost for Paula to come to your house. c) $50 per hour d) How much Paula charges per hour. e) 𝐶 = 75 + 50𝑛 f) $825 g) 21 hours 4) a) No initial value and the rate is not zero b) check with a peer
c) 𝐶 = 15 + 0.10𝑚 d) $25 e) 250 minutes 5) a) Same initial values b) Different rates
c) Line 1 : 𝐶 = 200 + 10ℎ and Line 2: 𝐶 = 200 + 5ℎ 6) a) F b) F c) T d) F e) T f) F g) F
7) 11 rides 8) 10 hours 9) Between $25 and $90 10) n = 25 to 56 and C = $1535 to $2961 11) a) 𝐸 = 80𝑛 + 520 b) Ilya could earn between $520 (if he didn’t sell any) and $1720 (if he sells 15)
Assignment 5.11: Linear Systems
1) Parallel Pines Bowling Alley offers two options. A graph representing the cost of Option A is shown on right. Option B charges $30 for unlimited bowling.
a) Draw Option B on the graph.
b) Decided if each statement is true of false i. Option B is always cheaper.
ii. Option A is cheaper for fewer than 15 games. iii. Option B is cheaper for fewer than 15 games. iv. Option A is an example of direct variation.
v. Option B is an example of direct variation. vi. Option B has a rate of $0/game
c) Write an equation to model each Option.
2) Two health clubs, Super Fit and Body Plus, offer monthly
memberships. The total monthly cost for each club is represented by the graphs below.
a) Write an equation for each health club. (Hint: determine the rate and initial value first)
b) Determine the conditions under which someone should choose each health club. Be specific.
3) Ariel and Hayden each have money in a bank account. Hayden’s weekly account balance is shown by the graph below. Ariel starts with $200 in her account and spends $20 each week, without making any deposits. Determine if the following statements are true or false.
a) Hayden deposits $10 each week.
b) Hayden will have less money in his account than Ariel in 6 weeks.
c) Hayden will always have more money in his account than Ariel.
d) Ariel starts with more money in her account than Hayden. e) Ariel has more money in her account than Hayden after 7
4) At Lowell High School, the cost to attend special events depends on whether or not a student has purchased a $10 discount card.
Option A The student buys a discount card. The cost is $5 per event.
Option B The student does not buy a discount card. The cost is $7.50 per event.
a) Create an equation to represent Option A and create an equation to represent Option B. Be sure to declare your variables
b) Graph the relationship between total cost and number of events for each option on the same grid. You may use a table of values if you wish.
c) Determine the conditions under which a student at Lowell High School should choose each option. Justify your answer.
5) Sales personnel at a sporting good store are given a choice of two options of pay. Plan A A monthly salary of $300, plus 2% commission on all sales Plan B No monthly salary, but a 5% commission on all sales.
a) Create an equation to represent Plan A and create an equation to represent Plan B. Be sure to declare your variables.
b) Graph the relationship between total sales and salary for each option on the same grid. You may use a table of values if you wish.
c) Determine the conditions when a sales personnel should choose each option. Justify your answer. 6. Serge is choosing a cellphone plan and wants the lowest cost. Cell-a-Bration charges $12 per month plus $0.05 per minute for cellphone service. E-Phone charges $28 per month for unlimited minutes. Determine under which conditions Serge should choose Cell-a-Bration and under which conditions Serge should choose E-Phone. Justify your answer.
7. Movies Are Us has two video rental plans. The Regular video rental plan charges $ 3.25 for each video rental. The Preferred video rental plan has an $ 8.75 membership fee and charges $ 2 for each video rental.
a) Write a system of equations to model the above situation. Define your variables.
b) How many video rentals give the two plans the same cost? What is the equal cost? Use mathematics to explain how you determined your answer. Use words, symbols or both in your explanation.
c) Which video plan costs more for 18 video rentals? Use mathematics to justify your answer. d) Which plan provides more videos for $ 30.00? Use mathematics to justify your answer
8. Carmen must choose between two different truck rental companies. Company A charges $80 to rent a truck, plus $0.20 per kilometer. Company B does not charge an initial fee, but charges $0.60 per kilometer.
a) Determine the equation for each company. b) Determine the point of intersection.
c) What does the point of intersection represent?
d) Determine under which conditions she should use each company. Answers Assignment 5.11: Linear Systems
1) a) check with a peer b) i. F ii. T iii. F iv. T v. F vi. T c) 𝐶 = 2𝑔 and 𝐶 = 30 2) a) Super Fit: 𝐶 = 40 and Body Fit: 𝐶 = 3𝑔 + 15
b) Before 8 visits body plus is cheaper, after 8 visit super fit is cheaper 3). a) T b) T c) F d) T e) F
4) a) Option A: 𝐶 = 5𝑒 + 10; Option B: 𝐶 = 7.50𝑒 b) check with a peer c) If a student is planning on going to less than 4 events, it’s cheaper to go with option B, if not, option A is cheaper. 5) a) Plan A: 𝐸 = 0.02𝑛 + 300 ; Plan B: 𝐸 = 0.05𝑛 b) Check with a peer c) If the sales personnel sells more than 10 000 worth of sporting goods, they should choose option B, if not, option A is better.
6) Cell-a-bration is cheaper before 320 minutes; E-phone is cheaper after 320 minutes.
7) a) Regular Video Rental Plan: 𝐶 = 3.25𝑛 ; Preferred Video Rental Plan: 𝐶 = 2𝑛 + 8.75 b) At 7 video rentals, both Rental Plans will cost $22.75
c) For 18 Rentals, the Preferred Rental Plan is $13.75 cheaper. 8) a) Company A: 𝑦 = 80 + 0.20𝑥; Company B: 𝑦 = 0.60𝑥 b) (200 km, $120) c) Both companies charge the same amount ($120) for the same distance (200 km) d) Choose Company A for 200 km or more. Chose
Assignment 5.12: Finding the Equation of A Line – Part 1: Given Slope and a Point on the Line
1) Find the equation of the line whose
a) slope is −5 and whose 𝑦-intercept is 5. b) slope is 2
3 and whose 𝑦-intercept is −2.
c) slope is −5
6 and whose 𝑦-intercept is− 2
3. d) slope is
1
8 and whose 𝑦-intercept is 8.
2) An equation of a line is 𝑦 = 2𝑥 + 𝑏. Find the value of 𝑏 if the line passes through the point…
a) (4,2) b) (−3,5) c) (2, −6) d) (−1, −3)
3) Write an equation of the line that passes through the given point and has the given slope. Express the equation in the form 𝑦 = 𝑚𝑥 + 𝑏 if possible.
a) (2, 3); 𝑚 = 4 b) (1, 4); 𝑚 = 3 c) (−5, 2); 𝑚 = 2 d) (3, −6); 𝑚 = −3
e) (−5, −1); 𝑚 = −2 f) (0, 7); 𝑚 = −1 g) (−6, 0); 𝑚 = 5 h) (5, 4); 𝑚 = 0
i) (1, −3); 𝑚 = 0 j) (2, 4); 𝑛𝑜 𝑠𝑙𝑜𝑝𝑒 k) (−3, 4); 𝑚 =1
2
4) Find the equation of a line….
a) with slope 4, passing through (1, 1) b) with slope 5, passing through (5, 0)
c) with slope 12 , passing through (8, 2) d) with slope −32, passing through (−3, −6) 5. Find the equation of each line in standard form.
a) Horizontal, passing through (3, 1) b) Vertical, passing through (3, 1)
c) Vertical, passing through (−2, 5) d) Horizontal, passing through (−2, 5)
e) Horizontal, through the origin f) Vertical, through the origin
6. Write an equation for the line, which passes
a) through the point (−11, −3) and which is parallel to 𝑦 = 8. b) through the point (−11, −3) and which is parallel to 𝑥 = 6. c) through the point (7, 8) and which is perpendicular to 𝑦 = −3. d) through the point (4, 5) and which is perpendicular to 𝑥 = 9.
Answers Assignment 5.12: Finding the Equation of A Line – Part 1: Given Slope and a Point on the Line 1) a) 𝑦 = −5𝑥 + 5 b) 𝑦 =23𝑥 − 2 c) 𝑦 = −56𝑥 −23 d) 𝑦 =18𝑥 + 8 2) a) 𝑏 = −6 b) 𝑏 = 11 c) 𝑏 = −10 d) 𝑏 = −1 3) a) 𝑦 = 4𝑥 − 5 b) 𝑦 = 3𝑥 + 1 c) 𝑦 = 2𝑥 + 12 d) 𝑦 = −3𝑥 + 3 e) 𝑦 = −2𝑥 − 11 f) 𝑦 = −𝑥 + 7 g) 𝑦 = 5𝑥 + 30 h) 𝑦 = 4 i) 𝑦 = −3 j) 𝑥 = 2 k) 𝑦 =1 2𝑥 + 11 2 4) a) 𝑦 = 4𝑥 − 3 b) 𝑦 = −𝑥 + 5 c) 𝑦 =1 2𝑥 − 2 d) 𝑦 = − 3 2𝑥 − 3 5) a) 𝑦 = 1, 𝑦 − 1 = 0 b) 𝑥 = 3, 𝑥 − 3 = 0 c) 𝑥 = −2, 𝑥 + 2 = 0 d) 𝑦 = 5, 𝑦 − 5 = 0 e) 𝑦 = 0 f) 𝑥 = 0 6) a) 𝑦 = −3 b) 𝑥 = −11 c) 𝑥 = 7 d) 𝑦 = 5
Assignment 5.13: Finding the Equation of A Line – Part 2: Parallel and Perpendicular Lines
1) Determine the equation of the line that is…
a) parallel to a line with slope 5, and through (−1, 6). b) perpendicular to a line with slope 2, and through (2, 5). c) perpendicular to 𝑦 =1
5𝑥, and through the origin.
d) parallel to 3𝑦 = 6𝑥, and through (−2, 3). e) perpendicular to 𝑦 − 𝑥 = 1, and through (3, 3).
f) parallel to the 2𝑥 − 𝑦 = 4 passes and through (−3, −11). g) perpendicular to the line 𝑦 =2
3𝑥 + 5 and that passes through (0, 4).
h) parallel to 𝑦 + 4𝑥 = 8 and passes through (2, 7). i) parallel to 𝑦 = 8 − 2𝑥 passing through (3, 7).
j) perpendicular to 3𝑦 = 5 − 2𝑥 passing through (4, 10).
2) Find an equation for the line perpendicular to 2𝑥 + 3𝑦 + 6 = 0, with the same 𝑦-intercept as 2𝑥 + 3𝑦 + 6 = 0
3) Find an equation for the line parallel to 3𝑥 + 5𝑦 − 4 = 0, with the same 𝑥-intercept as 2𝑥 − 3𝑦 − 6 = 0. 4) Given two lines whose equations are 3𝑥 + 𝑦 − 8 = 0 and −2𝑥 + 𝑘𝑦 + 9 = 0, determine the value of 𝑘 such that the two lines will be perpendicular.
5) A line passes through (2, 5) and (4, 0).
a) Use the coordinates of the two points on the line to find the slope. b) Use the slope from part a) and one of the points to find the y-intercept. c) Write an equation of the line.
Answers Assignment 5.13: Finding the Equation of A Line – Part 2: Parallel and Perpendicular Lines 1) a) 𝑦 = 5𝑥 + 11 b) 𝑦 = −1 2𝑥 + 6 c) 𝑦 = −5𝑥 d) 𝑦 = 2𝑥 + 7 e) 𝑦 = −𝑥 + 6 f) 𝑦 = 2𝑥 − 5 g) 𝑦 = − 3 2𝑥 + 4 h) 𝑦 = −4𝑥 + 15 i) 𝑦 = −2𝑥 + 13 j) 𝑦 =23𝑥 + 4 2) 𝑦 =52𝑥 − 2 3) 𝑦 = −35𝑥 +95 4) 𝑘 = 6 5) a) 𝑚 = −52 b) (0, 10) c) 𝑦 = −52𝑥 + 10
Assignment 5.14: Finding the Equation of A Line – Part 3: Given Two Points on the Lines
Find the equation of the line that passes through the given points.
1) (3, 2) and (6, −7) 2) (−5, −8) and (−7, −9) 3) (−1, −2) and (3, 0)
4) (3, −1) and (9, −5) 5) (−1, 4) and (3, 9) 6) (8, −7) and (−6, −7)
7) (0, 4) and (−5, 0) 8) (5, 2) and (5, −7)
9) A line passes through the origin and 𝐴(4, 6). a) Find the slope of the line.
b) Write an equation for the line.
10) A line has an 𝑥-intercept of 3 and a 𝑦-intercept of 4. a) Find the slope of the line.
b) Write an equation for the line.
11) Find an equation for a line with an 𝑥-intercept of −3 and a 𝑦-intercept of 5. 12) Find an equation for a line with an 𝑥-intercept of 4 and a 𝑦-intercept of −2.
13) Find an equation for a line with the same x-intercept as the line 2𝑥 + 5𝑦 − 4 = 0 and and the same 𝑦-intercept as the line 3𝑥 − 2𝑦 + 8 = 0.
14) Find an equation for a line with the same x-intercept as the line 3𝑥 − 4𝑦 + 6 = 0 and the same 𝑦-intercept as the line 4𝑥 − 5𝑦 − 10 = 0.
Answers Assignment 5.14: Finding the Equation of A Line – Part 3: Given Two Points on the Lines
1) 𝑦 = −3𝑥 + 11 2) 𝑦 =12𝑥 −112 3) 𝑦 =12𝑥 −32 4) 𝑦 = −23𝑥 + 1 5) 𝑦 =54𝑥 +214 6) 𝑦 = −7 7) 𝑦 =45𝑥 + 4 8) 𝑥 = 5 9) a) 𝑚 =32 b) 𝑦 =32𝑥 10) a) 𝑚 = −4 3 b) 𝑦 = − 4 3𝑥 + 4 11) 𝑦 = 5 3𝑥 + 5 12) 𝑦 = 1 2𝑥 − 2 13) 𝑦 = −2𝑥 + 4 14) 𝑦 = −𝑥 − 2
Assignment 5.15: Finding the Equation of A Line – Part 4: Applications
1. In Ottawa, you can ride on a tour bus for a fixed price plus a variable amount that depends on the length of the trip. The variable cost is $2/km and a 20-km trip costs $55
a) Determine the equation relating cost, C, in dollars, and distance, d, in kilometres. b) Use your equation to find the cost of a 15-km tour.
2. Emeline is driving at a speed of 100 km/h towards Hamilton for 2 h, when she sees the sign shown. a) What does the ordered pair (2, 300) mean?
b) The slope is 𝑚 = −100. What does this value represent? Why is it negative? c) Determine the value of 𝑏.
d) Write an equation relating distance and time.
e) Sketch the relation. What is the meaning of the d-intercept? f) How long will the car drive take, in total?
g) Has Emeline reached the halfway point of her trip yet? Explain.
3. Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of days that have passed.
a) Determine the amount of money he began with. b) Write an equation for the situation.
4. Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related.
a) What is the rate per minute?
b) What is the initial fee of this relationship?
c) What is the cost of a call of x minutes duration? (Assume this is linear relation) d) How long can you talk on the phone if you have $22 to spend?
5. A rain barrel full of water is drained at a constant rate. After 2 minutes, there is 70L of water remaining the in barrel. After 4 minutes, there is 40 L of water remaining.
a) How much water is in the barrel to start? b) Write an equation for this situation.
c) After 6 minutes, the draining is stopped. How much water is needed to refill the rain barrel? 6. There is a linear relationship between the total cost of renting a costume and the number of hours the costume is rented.
For 3 hours, the total cost is $60. For 5 hours, the total cost is $80. a) What type of variation is this relationship, and what is its initial value? b) Find a linear equation to model this situation.
7. A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes, the monthly cost will be $118.
a) Find a linear equation for the monthly cost of the cell plan as a function of x, the number of monthly minutes used.
b) Interpret the slope and vertical intercept of the equation.
c) Use your equation to find the total monthly cost if 687 minutes are used. d) If a customer paid $86.05, how many minutes did they use?
8) Consider the following table shown on right. a) Write an equation to represent this relation.
b) What temperature in degrees Celsius is equivalent to −20°𝐹?
Temperature in degrees Celsius, °𝑪 Temperature in degrees Fahrenheit, °𝑭 5 41 15 59 25 77
9) The graph below represents the relationship between the amount of water, A, in a pool as it drains and time, t.
a) What are the coordinates of two known points in this relationship?
b) Determine the rate of change of this relation. c) Determine the initial amount of water in the pool d) Write and equation to represent this relationship.
10) Karina has a job at a video store. The total she is paid each week is made up of an hourly rate plus $14 for transportation. One week, she works 20 hours and is paid $215.
a) Determine Karina’s hourly rate.
b) Write an equation represents this relationship
11) Alex has $150. She spends the same amount each week. After 6 weeks, she has $30 remaining. The relationship between the amount of money Alex has and the number of weeks is represented by a line. a) What is the slope of this line?
b) Write an equation represents this relationship 12) The table below shows information about the linear relationship between the total cost per month of Sylvie’s cellphone plan and the number of text messages she sends. According to this relationship, what is Sylvie’s total cost for March? Month Number of Text Messages, 𝒏 Total Cost, ($) January 60 28 February 20 24 March 30 ?
13) The total cost of a banquet includes a fixed fee to rent the hall and a cost per person. Information about the total cost at two different halls is shown below. Determine the cost to rent the hall.
Number of People, 𝒏 Total Cost, C, ($) 10 275 20 450 30 625
Answers Assignment 5.15: Finding the Equation of A Line – Part 4: Applications 1) a) 𝐶 = 2𝑥 + 15 b) $45
2) a) 2 hours into the trip, she is 300km away from Hamilton b) speed at which she is travelling towards Hamilton. c) 500km d) 𝐷 = −100𝑡 + 500 e) She started 500km away from Hamilton. f) 5 hrs
g) no, half way would be 250 km away from Hamilton.
3) a) $110 b) 𝐴 = −3𝑑 + 100
4) a) $0.99/min b) $0.96 c) 𝐶 = 0.99𝑥 + 0.96 d) approximately 21 minutes
5) a) 100 L b) 𝑉 = −15𝑚 + 100 c) 90L
6) a) Partial, the initial values is $30 b) 𝐶 = 20ℎ + 30
7) a) 𝐶 = 0.15𝑥 + 10 b) it cost $10 initially, then $0.15 every minute used c) $113.05 d) 507
8) a) 𝐹 = 1.8𝐶 + 32 b) −28.8 °𝐶 9) a) (20, 45 000) and (70, 0) b) 𝑚 = −900𝑚𝑖𝑛𝐿 c) 63 000 𝐿 d) 𝐴 = −900𝑡 + 63 000 10) a) $10.05ℎ b) 𝐸 = 10.05ℎ + 14 11) a) $ − 20 𝑤𝑒𝑒𝑘 b) 𝐴 = −20𝑤 + 150 12) $25 13) $100
