2. Does each situation represent direct variation or partial variation? a) Lily is paid $5 per hour for raking leaves.

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1 MPM1D Date: Name: Relating Linear Equations, Graphs and Table of Values 1. Alan works part-time at a gas station. He earns $10/h. His pay varies directly with the time, in hours, he works. a) Choose appropriate letter for variables. Complete the blanks. Circle the correct type of variable Let t be. Independent or Dependent? Let P be. Independent or Dependent? b) Complete the table of values showing Alan s pay. Graph this relationship. Are you going to connect the dots? Yes / NO c) Is the graph linear? YES / NO d) Does the graph pass through (0,0)? YES / NO e) Is it Direct or Partial Variation? f) Write an equation for the relation 2. Does each situation represent direct variation or partial variation? a) Lily is paid $5 per hour for raking leaves. b) The printing of brochures costs $250, plus $1.25 per brochure. c) Jordan is paid $30 per day, plus $2.00 for every magazine subscription he sells. 3. Does each equation represent a direct variation, a partial variation, or neither? a) C = 4n + 30 b) P = 4s c) d=65t d) d = t

2 4. The price charged to repair a computer is $ 20, plus $ 40/h. a) Identify the fixed cost (initial value) this company charges for fixing computers Fixed Cost = b) Choose appropriate letter for variables. Complete the blanks. Circle the correct type of variable Let t be. Independent or Dependent? Let C be. Independent or Dependent? c) Write an equation representing this relationship. d) Use the equation to graph relation without making a table of values. e) Are you going to connect the dots? Yes / NO f) Is the graph linear? YES / NO g) The graph pass through (0, )? h) Is it Direct or Partial Variation? i) What is the total cost of a repair that takes 3.5 hours? (use the graph to predict) 5. A rental car costs $30 per day plus $ 20 for each 100 km it is driven. a) Make a table of values for the rental fee up to 500 km. Graph the relationship. b) Write the equation that describes this relationship. c) Use the equation to determine how far you could go for $100. Confirm your solution using the graph.

3 6. Chris runs each day as part of his daily exercise. The graph shows his distance from home as he runs his route. a) Calculate his rate of change (speed) for each segment of the graph. Rate of change AB = Rate of change BC = Rate of change CD = Rate of change DE = Rate of change EF = b) Over what interval(s) of time is Chris travelling the fastest? 7. Two friends are leaving a parking lot at the same time. They agree to meet later at the home of a friend who lives 400 km from the parking lot. One friend drives a blue car and the other a red car. The blue car is labeled B and the red car, R. Answer the questions below using the following graph. a) At what time do the cars pass each other? How far are they from the parking lot? The cars pass each other 3 times. b) Which car stopped and for how long? How far from the parking lot did the car stop? c) Which car got to the final destination first? Explain. d) The posted speed limit was 80 km/h. If you were a police officer, could you stop either of the cars for speeding? Explain.

4 8. There is $500 in Holly s bank account. She takes out $50 from her account each month but doesn t put any back in. a) Make a table of values for up to 6 months. Graph the relationship. b) Write an equation to model the relationship. c) Does this relation represent a partial or direct variation? Explain. d) How much will Holly have in her account after 8 months? Show your work. e) How many months will have passed when Holly has $50 in her account? Show your work.

5 9. Nisha is just learning how to snowboard. White Mountain charges $10/hour for lessons and $30 for the lift ticket and snowboard rental. a) Make a table of values for up to 6 hours. Graph the relationship. b) Write an equation to model the relationship. c) Does this relation represent a partial or direct variation? Explain. d) How much will it cost in total for Nisha to take 2.5 hours of lessons? Show your work. e) If Nisha paid $75, how long was she at the White Mountain getting lessons? Show your work.