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5.6 Chapter summary

  • An ordered pair is made of two numbers, and the independent value always comes first. The coordinate pair, \((x; y)\), is an example of an ordered pair.
  • A table of values lists two groups of numbers:
    • The top row lists the independent values (or input values or \(x\)-values).
    • The bottom row lists the dependent values (or output values or \(y\)-values).
    • The numbers that are above and below each other are related to each other by the equation, and make an ordered pair.
    • The numbers that are above and below each other are related to each other by the equation.
  • A relationship between two quantities can be shown using a flow diagram, such as the one below. Each input number in a flow diagram has a corresponding output number. The first (top) input number corresponds to the first output number. The second input number corresponds to the second output number, and so on.
  • A completed flow diagram shows two kinds of information:
    • It shows what calculations are done to produce the output numbers.
    • It shows which output number is connected to which input number.
  • A formula is a mathematical relationship or rule expressed in numbers and letters. A formula is also an equation, which shows how the amounts are related to each other.
  • \(x\) is always the input value for an equation, and \(y\) is always the output value.
  • Each pair of \(x\)- and \(y\)-values that correspond to each other and make the equation true is called a solution of the given equation. A solution to the equation is an ordered pair that fits into the equation. In other words, a solution is a combination of \(x\)- and \(y\)-values that makes one side of the equation equal to the other side.