2. Ratios, Rates, and Proportions (N)
  3. Lesson 8: Proportionality in Tables and Graphs

Exercises


  1. A relationship between two quantities is shown in each table. Determine whether the table suggests a proportional relationship between the quantities.
    1. Number of Raffle Tickets Cost
      \(2\) \($ 6.00\)
      \(4\) \($12.00\)
      \(6\) \($16.00\)
    2. Cost Area (m\(^2\))
      \($5\) \(20\)
      \($25\) \(100\)
      \($ 62.50\) \(250\)
    3. Time (s) Distance (m)
      \(0\) \(0\)
      \(0.1\) \(5.2\)
      \(0.3\) \(15.6\)
      \(0.5\) \(26.0\)
  2. A relationship between two quantities is shown in each graph. Determine whether the graph suggests a proportional relationship.
    1. A graph with Time along the horizontal axis and Distance along the vertical axis. Five points are plotted at (1,2.5), (2,5), (3,7.5), (4,10), and (5,12.5).
    2. A graph with Number of Items along the horizontal axis and Cost along the vertical axis. Six points are plotted at (0,2), (1,5), (2,8), (3,11), (4,14), and (5,17).
    3. A graph with five points plotted at (1,0.5), (2,1), (3,1.5), (4,2), and (5,2.5).
  3. Consider the following table of values.
    \(x\) \(y\)
    \(3\) \(10.5\)
    \(4.5\) \(15.75\)
    \(6\)  
    \(7.5\) \(26.25\)
    If the relationship between \(x\) and \(y\) is proportional, then answer the following questions.
    1. What is the value of \(y\) when \(x = 6\)?
    2. What is the value of \(y\) when \(x = 100\)?
  4. Consider the following graph.
    A graph with Number of Items along the horizontal axis and Total Cost along the vertical axis. Four points are plotted at (5,15), (10,30), (15,45), and (20,60).
    If the total cost is proportional to the number of items, then answer the following questions. 
    1. What is the constant of proportionality, or the multiplicative relationship, between the number of items and the cost?
    2. What is the cost of \(17\) items?
    3. If the cost of \(N\)items is \($204\), then what is the value of \(N\)?
  5. Which of the following three graphs represents a proportional relationship with a constant of proportionality equal to \(\dfrac{5}{2}\)?
    1. A graph with four points plotted at (2,10), (4,20), (6,30), and (8,40).
    2. A graph with four points plotted at (4,5), (8,10), (12,15), and (16,20).
    3. A graph with four points plotted at (6,15), (12,30), (18.45), and (24,60).
  6. Various times and corresponding distances were recorded for a car travelling at a constant speed. At least one mistake was made when recording the data in the table below.
    Time (s) Distance (m)
    \(0\) \(0\)
    \(15\) \(180\)
    \(45\) \(590\)
    \(65\) \(780\)
    \(75\) \(900\)
    \(90\) \(1080\)
    \(120\) \(1400\)
    \(130\) \(1560\)
    \(150\) \(1800\)
    1. Graph the data.
    2. Which distances do you think were incorrectly recorded? What were the actual values?
    3. What is the constant speed of the car, in kilometres per hour?
  7. The following grid shows three graphs representing proportional relationships between \(x\) and \(y\).
    A graph with three lines. Line A has 3 points plotted at (1,0.5), (2,1), and (4,2). Line B has 3 points plotted at (1,2), (2,4), and (5,10). Line C has 3 points plotted at (2,8), (3,12), and (5,20).
    The constants of proportionality of the relationships are \(2\), \(4\), and \(\dfrac{1}{2}\). Match the constant of proportionality to the appropriate graph. Explain your reasoning.
  8. A spotted hyena and a cheetah are in a race. At full speed, the hyena can run at around \(18\) m/s and the cheetah can run at around \(33\) m/s. If the hyena has a \(435\) m head start, and both animals are running at full speed, then how long before the cheetah overtakes the hyena?