A graph
is a two-dimensional representation of a set of
numbers, or data.
TIME SERIES GRAPH
A time series graph
shows how a single variable changes over time.
GRAPHING TWO VARIABLES ON A CARTESIAN
COORDINATE SYSTEM
The Cartesian coordinate system
is the most common method of
graphing two variables. This
system is constructed by simply
drawing two perpendicular lines:
a horizontal line, or X-axis, and a
vertical line, or Y-axis. The axes
contain measurement scales
that intersect at 0 (zero). This
point is called the origin.
On a Cartesian coordinate system, the point at which the
graph intersects the X-axis is called the X-intercept.
The point at which the graph intersects the Y-axis is called
the Y-intercept.
The dotted line does not represent any data. Instead, it represents the
line along which all variables on the X-axis correspond exactly to the
variables on the Y-axis, for example, (10,000, 10,000), (20,000, 20,000),
and (37,000, 37,000). This line connecting all the points where
consumption and income would be equal.
The heavy blue line traces the data; the purpose of the dotted line is to
help you read the graph.
The slope of the line indicates whether the relationship
between the variables is positive or negative.
This line slopes upward,
indicating that there seems
to be a positive
relationship between
income and spending.
Points A and B, above the
45° line, show that
consumption can be
greater than income.
The slope of the line is computed as follows:
Y2  Y1
Y

X
X 2  X1
An upward-sloping line
describes a positive relationship
between X and Y.
A downward-sloping line
describes a negative relationship
between X and Y.
Changing Slopes Along Curves
Unlike the slope of a straight line, the slope of a curve is continually changing.
Figure 1A.5(a) shows a curve with a positive slope that decreases as you move from left to right.
Figure 1A.5(c) shows a curve with a negative slope that increases (in absolute value) as you move
from left to right.
In Figure 1A.5(e), the slope goes from positive to negative as X increases.
In Figure 1A.5(f), the slope goes from negative to positive. At point A in both, the slope is zero.