Linear+Relations+Problems

= Linear Relations / Slope (Questions)=
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1. Peter is a taxi driver. He charges a fixed cost of $3.25 and $0.50/km for every ride. a) Write the partial variation equation that describes his earnings for every ride. b) Graph the equation. c) Does the graph pass through the origin? Explain. d) How much money would he make if he drove a distance of 60 km? 105.5 km? 121 1/3 km [//ATaheri-Dezfouli//]

 2. Allison is saving the money she gets from allowance and her job at a fast-food restaurant to buy a car. She receives the same amount every month. After 5 months, she still needs to save $22 500. After 10 months, she still needs to save $20 000.

a) Graph the amount to be saved versus time. b) Is this a partial variation or a direct variation? Why? c) Write the equation for the relation. d) How much does the car Allison wants to buy cost? e) How much money does she receive per month? f) After how long would she have saved enough to buy a car? [//a_zhang//]

 3. Roger is repair man. He charges $100 plus $50 per hour fixing homes. a) Write a equation for this relation. b) Graph the relation. c) Is this a partial relation or direct relation? Why? d) If Roger worked for 5 hours, how much would he earn? [//m-yang//]

 4. Christopher likes to play World of Warcraft. However, it costs $50 dollars to register and make an account //and// he must pay $15 every month in order to play the game. a) Write an equation for the this relation. b) Is this an example of a direct variation or partial variation? c) Graph the equation. Personally, I find graphs annoying so you don't have to do this.  d) If it takes five years for Christopher to get over his addiction of this game (stop playing), how much money has he spent? e) If Christopher had $100 right before he registered and started playing //and// he gets $1 every week as an allowance, how long can he play the game for?   * f) If Christopher had $70 in the beginning instead //and// he gets $4 every week as an allowance, how much money does he have after one year? * <span style="display: block; color: rgb(0,0,0); font-family: Verdana,Geneva,sans-serif; text-align: right;">[//hli//]

<span style="font-family: Verdana,Geneva,sans-serif;"> 5. Brandon sets up a lemonade stand. The cost of set-up is $30.00. He sells each cup of lemonade for $1.00, and each cup of lemonade costs him $0.25 to make.

a) What is his profit for selling one cup of lemonade (excluding the set-up cost)? b) Is this an example of a direct variation or partial variation? c) Write an equation that describes his net earning (including the set-up cost). d) Graph the equation. e) What is the number of cups of lemonade that he must sell to break even (to have a profit of $0.00)? [A-Liu]

6. Bob earns $210 per week and 4% commission on all sales as a car salesperson. A car costs $7000. a) Write an equation for this relation. b) Is this an example of a direct or partial variation? c) Graph the equation. d) If Bob sells 7 cars/week, what are his weekly earnings? e) If Bob earns $6930 in a week, how many cars did he sell? f) Is it possible for Bob to earn $2030 in a week? Explain. [//jgnanapragasam//]

7. Jack wants a job at a office but first he must attend an interview. He buys a duotang for his interview which costs $5, he wastes $15 of gas getting to each interview. a) Write an equation that represent the money he wastes for the number of interviews he attends. b) <span style="background-color: rgb(255,255,255);">Graph this relationship. Is this a partial or direct variation question? Explain. c)If Jack attends 12 interviews, how much money has he wasted? d) If he gets a job at a place that is willing to pay him $1.15 a week if he works as a helper, how long will it take him to make up for the money he spent going to the 12 interviews? e) Is it possible for Jack to lose exactly $262 on interviews? Why or why not? f) If Jack decides that he will no longer take a duotang with him, how would the equation and graph change? [n_nandakumar]

8. Jenny works at a Stitches clothing store. She earns $400 per week and earns an extra $5 for every person she helps.

a) Write an equation for this relation. b) If Jenny helps 100 people in one week, what is her salary for the week? c) How many people would Jenny have helped if she earned $7200 for one month? d) What is the constant part in the equation? e) Is this a partial variation or a direct variation? f) Would the graph pass through the origin? [tShanmuganathan]

9.Zack earns 120 dollars per day. His daily expenses for his daughter Emily's private school is 8 dollars per hour.

a) Write an equation for the relation. b) State whether it is a partial or direct variation. Why? c) Graph the relation. d) If Emily goes to school for 6 hours, how much money is Zack left with at the end of the day? [//aashraf1//]

<span style="font-family: Verdana,Geneva,sans-serif;"> 10. David decided to go for a walk. He walks 10 metres in a minute. a) Write the direct variation equation to show the number of metres walked per minute. b) Graph the equation. c) How many metres will David walk in 170 minutes? d) How many minutes will it take David to walk if he walks 5 metres?

<span style="font-family: Verdana,Geneva,sans-serif;"> 11. A guy repairs cars. He charges a fixed cost of $45 and $20 for every 1 hour spent in working on it. a) Write the partial variation equation to show the the cost of fixing a car, in dollars, in terms with the time spent, in hours. b) Graph the equation. c) What will the cost of fixing the car be if the guy spends 5 hours repairing the car? d) How long would the guy have worked on the car if repairing it cost $85?

12. Tom Ketchup works at a leather coat store. He earns $250/week, plus a commission of 7% of his sales. a) Write an equation to describe her earnings for one week . b) Is this a partial variation equation or a direct variation equation. Explain. [//kobeaswaran//]

[Sabinnep]
//Edited by [S. Pranay]// //Edited by [ajeyarajah]//

b) Will it pass through the origin if graphed?
16. To post an advertisement on the Scarborough Mirror, there is a fixed cost of $10 and a fee of $5 for each day the ad runs. a) Write an equation to represent the cost of posting an ad. b) Is this a direct or partial variation? Explain. [S.Swamy]

17. Bob is a plumber. He charges $50 per hour of service. He also charges an additional fee of $60 for the usage of materials. a) Determine the equation. b) Is this a direct or partial variation? Why? [sshanmuganantham]

18. Water is poured into a water tank. In 5 minutes, 10 cm of the tank is filled. a) Express the relation between the time passed after the water started to be poured and the depth of the water filled within that time? b) How many centimetres is the depth of the water in the tank after 14 minutes? c) Is this a direct or partial variation? [N_anil]

19. Frank is playing with building blocks, and placing them on a base that is 4 cm in height. If Frank stacked 5 building blocks on top of each other (without the base), the tower would be 15 cm in height. a) Write an equation for this relation. b) Graph this equation, and state whether it is a direct or partial variation. [KXo]

20. Ron works at the local candy store. He earns $50 a day plus a commission of 10%. a) Write an equation for this problem. b) Graph this equation. c) Explain whether it is a direct or partial variation. [Kopeaswaran]

21. Dave is a babysitter and takes $10 per visit and $20 per hour. a)Write an equation for this problem. b)State whether this is a direct or a partial variation. Why? [CChitnis]

22. Bacteria reproduce by splitting into two new daughter cells about every half hour. a) If a bacterium began reproducing at 12:00, about how many bacteria would be present at: i) 3:00 p.m. ii) 6:00 p.m. iii) midnight b) Write an equation which represents the number of bacteria after (n) hours. [SLakkunarajah]

23. Three points on a line are (0, -8), (0, 60), and (0, 34). a) Find the slope. b) Write the equation in standard form. c) Write the equation in slope-y-intercept form. [//hli//]

24. A tractor costs $65 000. If its value each year is 85% of it value the previous year, find its value: a) after 7 years, to the nearest $100 b) after (n) years [Slakkunarajah]

25. If a cottage, originally bought for $30, 000, appreciates at the rate of 7% per year, what is it worth after: a) 3 years b) (n) years [Slakkunarajah]

26. Find the standard form of a line which passes through (9,7) and (-3,1). [kevink2435]

27. Determine the equation in standard form for the line parallel to 9x-6y+2=0 and passing through (7,3). [kevink2435]

28. If the lines kx-3y-10=0 and 2x-33y+9=0 are perpendicular, then find the value of k. [kevink2435]

29. Identify the slope of the line 7x-9y-2=0. [kevink2435]

30. In 1992, the population of a country called Kongland was 221. In 2000, the population number rose to 10021. Find the average rate of change to the nearest person per year. [kevink2435]

31. Find the equation in slope-y-intercept form of a line perpendicular to the line 9x-9y-9=0 and having the same y-intercept as the line 7x-7y-6=0. [kevink2435]

32. The cost of purchasing a Ferrari is $2009/vehicle plus $250. a) Write the equation of this relation. b) Create a table of values c) Graph the relation d) Graphically find the cost of buying 140 Ferraris. [kevink2435]

33. The equation of a line is 2x-qy-r=0. The slope is 9 and the y-intercept is 3. What are the values of q and r. [kevink2435]

34. An equation of a line is Jx-5y+6=0. If the line passes through (15,8), then what is the value of J? [kevink2435] and [A-Liu]

35. Tom Ketchup is a plumber. He charges a fixed cost of $45 and $14 per hour. He wants to buy a gingerbread bike that costs $535 plus tax. How many hours would he have to work for to buy the bike? To complete this answer, use a table of values and the graph it. [kevink2435] and [A-Liu] <span style="color: rgb(0,0,0);">

36. Find the equation of the line with the same slope as the line 2x+4y+1=0 and passes through the point (7,-3) <span style="display: block; color: rgb(0,0,0); text-align: right;">[kevink2435] and [A-Liu]

37. Find the equation in standard form for the following pairs of ordered pairs. a) (4,3) and (-7,4) b) (0,-1) and (-3,4) c) (6,-4) and (4,-2) [kevink2435] and [A-Liu]

38. The equations of two lines are y = ¾x - 7 and 9x + 2 = 0. a) Calculate the point of intersection. [//hli//]

38. a) List the Domain and Range for the ordered pairs. b) Write an equation for the relation. c) Graph the relation. [Apasricha]
 * X || Y ||
 * 1 || 14 ||
 * 2 || 28 ||
 * 3 || 42 ||
 * 4 || 56 ||

39. Draw the graphs of the following lines. Identify whether the slopes of the lines are negative, positive, zero, or undefined.

a) y = 4x + 10 b) 45x + 15y -5 = 0 c) x = - 3 d) y = 11 [Apasricha]

40. Lara is running for the position of vice president on the SLC. As part of her campaign she must make posters. Lara prints 250 posters that cost 815 dollars. If it costs 3 cents per poster plus and additional fixed cost

a) What is the fixed cost? b) create a table of values using the equation of the relation. c) Graph the relation. What is the p-intercept and what does it represent? d) Using the graph determine the number of poster she printed if it had cost her $ 434? [Apasricha]

41. Find the slope and y- intercept of he line that passes through the points ( -6,3 ) and ( 1,2 ). Then write the equation of the line in standard form. [Apasricha]

42. When the slope of a line is - 1/2 and on point on the line is ( - 4,8 )

a) Find the equation of the line. b) Using the equation find the y- intercept and the x- intercept of the line. [Apasricha]

43. State the line parallel to 4x + 7y - 3 = 0 and passing through the point ( 3, 5 ). [Apasricha]

44. If two perpendicular lines have the same x- intercept. Line one of the lines the slope is 5 and the two points on that line are ( 3, 0 ) and ( 0,9 ). Find an equation for line two. [Apasricha]

45. Plot the points ( 4,8 ), ( 3,2 ), ( - 2,1 ), ( 6,4 ), ( 5,6 ), ( 1, - 2 ) and ( 4,2 ) on a grid. a) Draw the line of best fit. b) Find the slope of the line of best line. c) Using the slope and a point on the line find an equation for the line, and convert it to point-slope form. d) If there was a line perpendicular to the line of best fit what would it's slope be? [Apasricha]

46. A dudette earns $412/day plus 21% commission on sales. a) Write the equation of the relation. b) Create an appropriate table of values. c) Graph the relation. d) Graphically find the salesperson's earnings when sales are a total of $485.50. [y_yuan]

47. Find the standard form of the line which passes through (-12,4) and has a slope of 1/4. [y_yuan]

48. Given the point (1,-5) and (-2,4) find the slope. [y_yuan]

49. Here are two points: (8, 7) (-7, -4) Find the slope. [kevink2435]


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