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 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.

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 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.

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.