Mathematics: Variation and Graphs

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Questions and Answers

What is Direct Variation?

  • A relationship that cannot be expressed mathematically
  • A relationship where the increase of one variable results in a decrease of the other
  • A relationship where one variable is a constant multiple of the other (correct)
  • A relationship where both variables are independent

What is Inverse Variation?

  • When both variables are zero
  • When one variable changes, the other remains constant
  • When one variable increases and the other decreases (correct)
  • When both variables increase together

What is an equation or function that represents a straight line?

Linear

A non-linear function forms a straight line.

<p>False (B)</p> Signup and view all the answers

What is represented by the slope of a line?

<p>Rate of Change</p> Signup and view all the answers

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Study Notes

Direct Variation

  • Represents a relationship where one variable is a constant multiple of another.
  • Changes in one variable result in proportional changes in the other variable.

Inverse Variation

  • Defined as the opposite of direct variation.
  • When one variable increases, the other decreases proportionally.
  • The product of the two variables remains constant despite their individual changes.

Linear

  • Describes an equation or function that produces a straight line on a graph.
  • Formulated as ( y = mx + b ), where ( m ) indicates the slope and ( b ) is the y-intercept.

Non-linear

  • Refers to equations or functions that do not create a straight line.
  • Includes curves and other shapes, indicating varying rates of change.

Rate of Change

  • Quantified by the slope of a line in a linear graph.
  • Represents how one quantity changes in relation to another variable.

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