Unit D: Graphing

Practice


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  1. Natasha bought a new truck and wanted to check the truck's mileage. In the following table of values, she recorded the distance she travelled after using specific amounts of gasoline.

    Gasoline Used (L)
    		25 50 75 100
    Distance Travelled (km)
    		202 404 606 808

    1. Identify the dependent variable and the independent variable.

    2. Is the data discrete or continuous? Justify.

    3. Graph the data.

      Be sure to include
      • an appropriate scale
      • the labelled axes (including units)
      • the dependent variable on the y-axis and the independent variable on the x-axis
      • a title
      • a line connecting points when applicable (continuous: yes; discrete: no)

    4. Does the graph represent a linear relation? Justify.

  2. Kyle works 4 to 6 hours per day and is paid $15/hour at 30 minute intervals.

    1. Identify the dependent and the independent variable.

    2. Complete the table of values when Kyle works 4.0, 4.5, 5.0, 5.5, and 6 hours.

      Hours Worked
      		Pay ($)
      4.0
      4.5
      5.0
      5.5
      6.0


    3. Is the data continuous or discrete? Should the points be connected? Explain.

    4. Graph the data.

      Be sure to include
      • an appropriate scale
      • the labelled axes (including units)
      • the dependent variable on the y-axis and the independent variable on the x-axis
      • a title
      • a line connecting points when applicable (continuous: yes; discrete: no)

    5. Does the graph represent a linear relation? Justify.

    Natasha bought a new truck and wanted to check the truck's mileage. In the following table of values, she recorded the distance she travelled after using specific amounts of gasoline.

    Gasoline Used (L)
    		25 50 75 100
    Distance Travelled (km)
    		202 404 606 808

    1. Identify the dependent variable and the independent variable.

    2. Is the data discrete or continuous? Justify.

    3. Graph the data.

      Be sure to include
      • an appropriate scale
      • the labelled axes (including units)
      • the dependent variable on the y-axis and the independent variable on the x-axis
      • a title
      • a line connecting points when applicable (continuous: yes; discrete: no)

    4. Does the graph represent a linear relation? Justify.

    1. Since the distance travelled is dependent on the volume of gasoline used, the gasoline used is the independent variable (x-axis) and the distance travelled is the dependent variable (y-axis).

    2. The data is continuous since the values in between the points are valid in this situation. It is possible to use a fraction of a litre of gasoline or travel part of a kilometre.




    4. The graph represents a linear relation because the line drawn is straight, and a general trend can be seen.
    Kyle works 4 to 6 hours per day and is paid $15/hour at 30 minute intervals.

    1. Identify the dependent variable and the independent variable.

    2. Complete the table of values when Kyle works 4.0, 4.5, 5.0, 5.5, and 6 hours.

      Hours Worked
      		Pay ($)
      4.0
      4.5
      5.0
      5.5
      6.0


    3. Is the data continuous or discrete? Should the points be connected? Explain.

    4. Graph the data.

      Be sure to include
      • an appropriate scale
      • the labelled axes (including units)
      • the dependent variable on the y-axis and the independent variable on the x-axis
      • a title
      • a line connecting points when applicable (continuous: yes; discrete: no)

    5. Does the graph represent a linear relation? Justify.

    1. Since the pay earned is dependent on the number of hours worked, the number hours worked is the independent variable (x-axis) and the pay earned is the dependent variable (y-axis).

    2. Multiply the hours worked by the hourly rate to find the amount of pay earned. When Kyle works 4 hours, Kyle earns 4 Ã— $15.00 = $60.00.

      The table of values below shows Kyle's hours work and daily pay.

      Hours Worked
      		Pay ($)
      4.0
      60.00
      4.5
      67.50
      5.0
      75.00
      5.5
      82.50
      6.0
      90.00

    3. The data is discrete since Kyle will not be paid for amounts between the points. The points should not be connected.


    4. The graph can also be drawn without the breaks in the axes.


    5. This is a linear relation because the points form a shape of a straight line. The graph represents a linear relation because if the points were connected, a straight line would be formed. However, the points are not connected in this scenario as the data is discrete and not continuous.