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 “dependent variable”.

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.

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.

Direct Proportions Two quantities are directly proportional to 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.

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).

Inverse Proportions Two quantities are inversely proportional to 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.

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.