Properties of a Straight-line Graph
65
3. Do not place the "zero" or origin of the coordinate system at one
corner of the graph paper if doing so would make a small, cramped,
inconvenient scale.
4. Label the axes (the vertical axis is the ordinate, the horizontal axis the
abscissa) with both units and dimensions.
5. When possible and desirable, simplify the scale units in order to use
simple figures. For example, if you wanted to plot as scale units 1000
min, 2000 min, 3000 min, 4000 min, etc., it would be simpler to use the
figures 1, 2, 3, 4, etc. and then label the axis as min x 10~
:! . Such
labeling states that the actual figures (in minutes) have been multiplied
by 10~
;i in order to give the simple figures shown along the axis.
6. Draw a smooth curve that best represents all the points; such a curve
may not necessarily pass through any of the points. Straight-line segments should not be drawn between consecutive points, unless there is
a reason to believe that discontinuities (angles) in the curve really do
occur at the experimental points; such reasons almost never exist.
PROPERTIES OF A STRAIGHT-LINE GRAPH
Whenever possible, cast data into such a form that a straight-line graph results
from their plotting. A straight line is much easier to draw accurately than a
curved one; often one can obtain important information from the slope or
intercept of the straight line. If the two variables under discussion are* andy
(the convention is to plot x as the abscissa andy as the ordinate), and if they are
linearly related (i.e., if the graph is a straight line), the form of the mathematical
equation that represents this line is
y = mx + b
(6-1)
No matter what the value of m, when,v = 0, theny = b. It is for this reason that
b is called the "y intercept," the point at which the line intersects they axis (see
Figure 6-1).
If two arbitrary points (x lt y J and (x 2 , >' 2 ) are selected from this line, both sets
of points must satisfy the general equation for the line. Consequently, we have
two specific equations:
y 2 = mx 2 + b
(6-2)
and
y, = mx t + b
(6-3)
If we subtract the second equation from the first, we obtain
y 2 - yi = mx 2 - mx t = m(x 2 - x t )
(6-4)
65
3. Do not place the "zero" or origin of the coordinate system at one
corner of the graph paper if doing so would make a small, cramped,
inconvenient scale.
4. Label the axes (the vertical axis is the ordinate, the horizontal axis the
abscissa) with both units and dimensions.
5. When possible and desirable, simplify the scale units in order to use
simple figures. For example, if you wanted to plot as scale units 1000
min, 2000 min, 3000 min, 4000 min, etc., it would be simpler to use the
figures 1, 2, 3, 4, etc. and then label the axis as min x 10~
:! . Such
labeling states that the actual figures (in minutes) have been multiplied
by 10~
;i in order to give the simple figures shown along the axis.
6. Draw a smooth curve that best represents all the points; such a curve
may not necessarily pass through any of the points. Straight-line segments should not be drawn between consecutive points, unless there is
a reason to believe that discontinuities (angles) in the curve really do
occur at the experimental points; such reasons almost never exist.
PROPERTIES OF A STRAIGHT-LINE GRAPH
Whenever possible, cast data into such a form that a straight-line graph results
from their plotting. A straight line is much easier to draw accurately than a
curved one; often one can obtain important information from the slope or
intercept of the straight line. If the two variables under discussion are* andy
(the convention is to plot x as the abscissa andy as the ordinate), and if they are
linearly related (i.e., if the graph is a straight line), the form of the mathematical
equation that represents this line is
y = mx + b
(6-1)
No matter what the value of m, when,v = 0, theny = b. It is for this reason that
b is called the "y intercept," the point at which the line intersects they axis (see
Figure 6-1).
If two arbitrary points (x lt y J and (x 2 , >' 2 ) are selected from this line, both sets
of points must satisfy the general equation for the line. Consequently, we have
two specific equations:
y 2 = mx 2 + b
(6-2)
and
y, = mx t + b
(6-3)
If we subtract the second equation from the first, we obtain
y 2 - yi = mx 2 - mx t = m(x 2 - x t )
(6-4)