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Graphing

Graphing. What does graph represent?. A graph represents the relationship between a pair of variables. The variable which is changed in a controlled manner in an experiment is called the “ independent variable”, while the variable which responds to this change is called the

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Graphing

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  1. Graphing

  2. What does graph represent? • A graph represents the relationship between • a pair of variables.

  3. The variable which is changed in a controlled manner in an • experiment is called the “independent variable”, while the • variable which responds to this change is called the • “dependent variable”.

  4. dependent variable independent variable • As a matter of form, the independent variable is plotted on • the horizontal, or x-axis, while the dependent variable is plotted • on the vertical, or y-axis.

  5. Once the data points have been plotted, the line best • represented by the point is drawn. • Due to experimental uncertainty and error, the data points will • not lie exactly on this line. • The drawing of a line is the equivalent to taking a weighted • average of the data points.

  6. Direct Proportions • Two quantities are directly proportionalto each other if dividing one by the other gives a constant value. • read as “y is proportional to x.” • The general equation for a directly proportional relationship • between the two variables can also be written as follows: The value of k is a constant called the proportionality constant.

  7. Direct Proportion When mass is divided by volume the result is a constant value. Note: All directly proportional relationships produce graphs that pass through the origin. Remember for a direct proportion “y” divided by “x” is equal to a constant (k).

  8. Inverse Proportions • Two quantities are inversely proportionalto each other if their product is constant. • read as “y is proportional to 1 divided by x.” • The general equation for an inversely proportional relationship • between the two variables can be written in the following form: • xy = k • In the equation, k is the proportionality constant. If x increases, • y must decrease by the same factor to keep the product constant.

  9. Inverse Proportion • A graph of variables that • are inversely proportional • produces a curve called • a hyperbola. Notice if we multiply pressure (x) by volume (y) we obtain a constant value.

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