Review Topics for Success

prerequisite Learning Outcomes

Note: Before studying voting theory, it will be good to first embark on an in-depth exploration of graphs. While these prerequisites are not directly related to the Learning Outcomes of Voting Theory, they will assist in the assessment and analysis of election data.

By the end of this prerequisite section, you will be able to:

  • Locate an object on a map using coordinate directions
  • Plot points on a rectangular coordinate system
  • Identify the quadrant where a point is located on a rectangular coordinate system
  • Name the ordered pair of a point on a coordinate system
  • Given a coordinate pair, determine whether it is a solution to a two variable equation
  • Complete a table of values that satisfy a two variable equation
  • Find any solution to a two variable equation
  • Identify the x and y-intercepts of a line given in equation form
  • Identify the x and y-intercepts of a line given in graph form
  • Use intercepts to graph a line
  • Use intercepts combined with a third point to graph a line
  • Determine the most convenient way to graph a line given it’s equation
  • Use a model to determine slope
  • Create a model of slope
  • Given the graph of a line, determine the slope of the line
  • Identify the slope of a horizontal or vertical line given it’s equation
  • Find the slope of a line given two points on the line
  • Graph a line given the slope and a point on the line
  • Solve slope applications.

Suppose a group of data has been collected, such as tallies of choices made by voters. The information arising from that data needs to be presented to interested parties in a useful way. Data presentation, the organization of collected data into objects such as tables and graphs, requires attention to both the quantitative or statistical analysis of the data and the perspective that the organization of the data implies. While several different styles of data presentation exist, voting data is frequently presented in the form of a table of rows and columns containing two variables: a candidate and that candidate’s polling outcome. This sort of relationship in two variables is closely related to another form of data representation in a space called the coordinate plane in which the two variables are related together in an ordered pair called a data point. For election data, the ordered pair of variables might take the form of (candidate, polling outcome). The same data can be presented in tabular form in rows and columns or graphical form as data points in a plane. We will also take an introductory look at equations by studying the equation of a line between two data points in the plane.

Recall for success

Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.