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23.7 Chapter summary

  • An independent variable is not affected by changes in the other variable in a relationship.
  • A dependent variable is influenced by the other variable, and changes depending on the relationship with the other variable.
  • A linear graph (also called a straight-line graph) shows that the relationship between the independent variable and dependent variable is a straight line.
  • For an increasing graph, the dependent variable increases as the independent variable increases.
  • For a decreasing graph, the dependent variable decreases as the independent variable increases.
  • For a constant linear graph, the dependent variable does not change as the independent variable increases.
  • The maximum point on a graph is the point where the dependent variable has the greatest value.
  • The minimum point on a graph is the point where the dependent variable has the smallest value.
  • Discrete data is made up of quantities that have been counted.
  • The plotted points on a discrete graph are not joined by a line.
  • Continuous data is made up of quantities that have been measured.
  • The plotted points on a continuous graph are joined by a line or curve.
  • The Cartesian coordinate system consists of two axes.
  • The \(x\)-axis is a horizontal line at \(y = 0\).
  • The \(y\)-axis is a vertical line at \(x = 0\).
  • The point where the two lines intersect is called the origin, (0; 0).
  • The \(x\)-axis and the \(y\)-axis divide the Cartesian plane into four quadrants.
    • In the first quadrant (I), the values of the \(x\)-axis are positive and the values of the \(y\)-axis are also positive.
    • In the second quadrant (II), the values of the \(x\)-axis are negative and the values of the \(y\)-axis are positive.
    • In the third quadrant (III), the values of the \(x\)-axis are negative and the values of the \(y\)-axis are also negative.
    • In the fourth quadrant (IV), the values of the \(x\)-axis are positive and the values of the \(y\)-axis are negative.
  • An ordered pair consists of an \(x\)-value called the \(x\)-coordinate and a \(y\)-value called the \(x\)-coordinate. Notation: \((x; y)\)