Drawing graphs
LINEAR GRAPHS
Used to graph relationships which are linear, that is where values on the
vertical axis (y values) are directly proportional to values on the horizontal
axis (x values). Linear graph paper has divisions on each axis which are evenly
distributed.
The result is a straight line represented by the equation: 
y = mx + b
where m is the slope of the line and b is the intercept on the y axis. If the line is at a 45o angle then the slope is 1. With a slope of 1, y is directly proportional to x, as you double x you also double y. If the slope is 2, then as you double x, you increase y by 4 times.
A straight line implies that the proportion between two values is the same for values on the x axis and on the y axis i.e. :
y1/y2 = x1/x2
If you know any three of these values, you can determine the fourth, for
example in a colorimetric assay
absorbance test =
concentration test
absorbance standard concentration
standard
If you know the concentration of a standard, and measure the absorbance of it
and a test specimen, then you can calculate the concentration of the test sample
from the relationship given above. This of course, is only true for straight
line graphs.
SEMI-LOG GRAPHS
When some sets of data are graphed on linear graph paper, they show an exponential relationship. This is because one variable (usually on the y axis) is increasing at an exponential rate while the other variable is increasing at a linear rate. The result is a graph like this:
To make this into a straight line, plot the values on semi-log paper, with those increasing (or decreasing) in an exponential fashion on the log scale and those increasing (or decreasing) in a linear fashion on the linear scale. You can obtain 1 cycle, 2 cycle or 3 cycle paper which gives you an effective range of from 1 to 1000 on the y axis. Where there is more than one cycle on the paper, each cycle must be ten times the previous one and each must represent an entire order of magnitude. If you have values between 1 and 10 or between 10 and 100 or any set of values between multiples of 10, you can use one cycle. If your values are from 1 to 10 and from 10 to 100, or between any two multiples of 10, you use 2 cycles. If your values are from 1 to 10, 10 to 100 and 100 to 1000, or between any three multiples of 10, you use 3 cycles. Notice that in each cycle, as the values get larger, the lines get closer together. This means that the exponential part of the curve shown above becomes “flattened” out to produce a straight line. Once you have a straight line standard graph you can interpret test values from it in the same way as for linear standard graphs. One application for semi-log graphs in Microbiology is in the biological assay of antibiotics e.g. gentamicin.
Double log graphs
Double log paper has a log scale on both axes, and is used for graphs where both sets of variables are changing in an exponential fashion. There are not many applications for this type of graph in biological sciences. The example shown is 2x1 cycle log-log paper. As with semi-log paper, one cycle is used for each order of magnitude i.e. 1 to 10, 10 to 100 etc.
Examples of Log Graph Paper
1. 1 Cycle Semi-log
2. 2 Cycle Semi-log
3. 2 Cycle Double Log
