Line graphs

A typical plot of x vs./(x) is considered to have one coordinate dimension, the X, and one data dimension,/(x). These data sets are plotted as line graphs, bar graphs, and so forth. These types of plots are readily made with most spreadsheet programs as well as dedicated graphing programs. Figure 13.1 shows two graphs that are considered to have a one-dimensional data space. 

Quite often isochronous data is presented on log-log scales. One of the reasons for this is that on linear scales any slight, but possibly important, non-linearity between stress and strain may go unnoticed whereas the use of log-log scales will usually give a straight-line graph, the slope of which is an indication of the linearity of the material. If it is perfectly linear the slope will be 45°. If the material is non-linear the slope will be less than this. 

The straight line graph of stress against log (time) confirms the relationship... 

If the kinetics of the reaction disobey the Michaelis-Menten equation, the violation is revealed by a departure from linearity in these straight-line graphs. We shall see in the next chapter that such deviations from linearity are characteristic of the kinetics of regulatory enzymes known as allosteric enzymes. Such regulatory enzymes are very important in the overall control of metabolic pathways. 

Charles and Gay-Lussac carried out a number of experiments with the hope of improving the performance of their balloons. They found that, provided the pressure is kept constant, the volume of a gas increases as its temperature is raised. In this case, a straight-line graph is obtained when the volume is plotted against the temperature (Fig. 4.10). This result implies... 

The formula of a straight-line graph of y (the vertical axis) plotted against x (the horizontal axis) is... 

Many of the equations that we meet in the text can be rearranged to give a straight-line graph when plotted as shown in the following table. 

FIG. 76. Frequency response characteristics of a conventional, graphite-coaled diaphragm (bar graph) and an o-Si H-coated diaphragm (line graph). 

The results of an experiment are often shown on a graph that displays the data that has been collected. Graphs can make known facts easier to understand and analyze. With a line graph, it is possible to estimate values for points that fall between those actually measured. This process is called interpolation. Graphs can also be used to estimate data points beyond the measured points through a process called extrapolation. 

The dependent variable is plotted on the vertical axis of a line graph, which is called the y-axis. The quantities displayed on this axis reflect the changes that take place or depend upon the way the experiment is performed. The independent variable is plotted on the horizontal axis of a graph, which is the x-axis. 

In this activity, you will collect data and draw a line graph. Be certain that your graph is neat and easy to read. Use a sharp pencil to establish points and draw a fine line. 

Explain why a line graph might not be appropriate to show the chemical composition of Earth s crust. 

An intuitive way to measure the rate constant, k, is to prepare some number of molecules in the excited state, perhaps with a pulse of light, and observe the amount of light given off per unit of time after the pulse. A logarithmic plot of intensity with time will give a straight-line graph with a slope of -k. This approach is the basis of time domain measurements. 

Fig. 4 Data on pollutant burden and its effects on fish in the low Ebro River, from Riba-roja to Xerta. (a) Total PCB content in sediments from Riba-roja (reference site), Flix, Asco, and Xerta in ng/g (green bars). Superimposed to this profile, line graphs indicate median values for three markers related to...

For the straight-line graph of Rate versus [Enzyme], an excess of substrate must be present. 

Figure 1. a) Quantum graph b) periodic path on a graph with quantum weights defined with respect to the line - graph. 

The adjacency matrix ALG of the line-graph of G can then be written in the form (Severini 2003, Severini and Tanner 2004)... 

Figure 5.19 Arrhenius plot of diffusion data, In D versus 1/T. The slope of the straight-line graph allows the activation energy of diffusion, a, to be determined, and the intercept at 1/T = 0 gives a value for the pre-exponential factor.

Figure S5.1 Straight-line graph of In c versus x2 from a diffusion experiment The slope of the graph allows a value for the diffusion coefficient, D, to be determined.

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