Unit D: Graphing

Sketching a Graph

It is important that a graph is easy to plot and properly displays data. Most of the graphs sketched in this unit will only include Quadrant 1 (the top right-hand corner of the Cartesian plane).




To ensure success when sketching Quadrant 1 graphs, follow the instructions below:

  • Draw the horizontal and vertical axes. Leave room to the left of the vertical axis and below the horizontal axis for labels and numbers.

  • Put the independent variable on the x-axis (horizontal axis) and the dependent variable on the y-axis (vertical axis) using an appropriate scale. The scale must be uniform (equally spaced). Scales are selected so that the graph covers as much of the page as possible. The horizontal axis scale and interval size can differ from the vertical axis scale and interval size because each axis represents a different variable.

  • Label each axis according to the information or variable that it represents. The units should be included in round brackets.

  • Connect the points if the data is continuous. Do not connect the points if the data is discrete.

  • Title the graph.

A graph can easily be drawn if a table of values is given.

The table of values below represent the cost of renting movies from an online store.

Number of
Movies Rented
Cost (dollars)
1 3.50
2 7.00
3 10.50
4 14.00
5 17.50
6 21.00

  1. Identify the dependent variable and the independent variable.

  2. Should the points on the graph be connected? Explain.

  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. The cost of the movies is dependent on the number of movies rented. Therefore the number of movies is the independent variable (x-axis) and the cost of renting the movies is the dependent variable (y-axis).

  2. It is not possible to rent 1.5 movies or 2.75 movies. The values between the points on the graph are not valid so the data is discrete and the points should not be connected.




  4. This is a linear relation, because the points form the shape of a straight line. However, the points are not connected as the data is discrete and not continuous.
The data represented in the table of values was collected from five students who volunteered for a study investigating the relationship between exam results and study time which was completed in 30 minute intervals.

Study Time
(minutes)
Exam Results
(%)
30 75
60 45
90 80
120 87
150 92

  1. Identify the dependent variable and the independent variable.

  2. 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)

  1. The dependent variable is the exam result and the independent variable is the study time. The exam result is dependent on the study time.

  2. A line connecting the points should not be drawn. The values between the points should not be included in the graph as a student only studies in half hour intervals.




    For the Exam Mark versus Study Time graph, there is no data below 30 minutes on the x-axis and no data below 45% on the y-axis. This creates wasted spaced on the graph. Breaks in the axes can be used to shorten the unnecessary portions of the axes between the origin and the first data value.




    The “squiggle” symbol ( ) on the graph above is called an axis break. There are two axis breaks on the Exam Mark versus Study Time graph. The break on the x-axis represents that there are many numbers between the values of 0 and 30. The break on the y-axis represents that there are many numbers between 0 and 40. Axis breaks can be used to exclude unnecessary parts of a graph.