Using Line Graphs

In your study of chemistry, the most common curves are the linear, representing the direct relationship (y oo x), and the inverse, representing the inverse relationship (y oo 1/x), where x represents the independent variable and y represents the dependent variable. In a direct relationship, y increases in value as x increases in value, or y decreases when x decreases. In an inverse relationship, y decreases in value as x increases. 

An example of a typical direct relationship is the increase in volume of a gas with increasing temperature. When the gases inside a hot-air balloon are heated, the balloon gets larger. As the balloon cools, its size decreases. However, a plot of the decrease in pressure as the volume of a gas increases yields a typical inverse curve. 

Infer Nhat would an almost flat line indicate  

The linear graph is useful in analyzing data because a linear relationship can be translated easily into equation form using the equation for a straight line. 

In the equation, y stands for the dependent variable, m is the slope of the line, x stands for the independent variable, and h is the y-intercept, the point where the curve crosses the y-axis. 

The shape of the curve formed by a plot of experimental data indicates how the variables are related. 

Number of half-lives (1 half-life = 29 years) 

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Scientists, such as the one in Figure 13a, as well as you and your classmates, use graphing to analyze data gathered in experiments. Graphs provide a way to visualize data in order to determine the mathematical relationship between the variables in your experiment. Most often you use line graphs. 

Never use line graphs. Line graphs are graphs that use an arbitrary x-axis scale having equal spacing between consecutive data points. Figure 28.8 illustrates this type of graph. These... 

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. 

Isotherm A line in a flow system or on a graph connecting points of equal temperature, or a mathematical or graphical relationship between two variables at constant temperature. Or a display using lines on a drawing to show constant-temperature contour lines, as from thermal imaging with infrared techniques. 

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. 

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. 

The central purpose of a graph is to present, summarize, and/or highlight trends in data or sets of data. Graphs of various types (e.g., scatter plots, contour plots, two- and three-dimensional line graphs, and bar graphs) are used for different purposes thus, authors must match their purpose with the appropriate type of graph. 

Figure 16.1 (Before correction) Examples of common formatting errors in line graphs (Figure 1) and bar graphs (Figure 2). (Note The authors used red and blue symbols in Figure 1 blue, red, and purple bars in Figure 2 and gray backgrounds.)...

Here is the same information presented as a line graph. This type of graph uses two axes, rather than columns and rows, to create a visual representation of the data. 

Scatter Diagram A scatter diagram is a basic tool to identify the potential relationship between two variables. Scatter diagrams are similar to line graphs in that they use horizontal and vertical axes to plot data points. Flowever, they have a very specific purpose. Scatter diagrams show how much one variable is affected by another. The relationship between two variables is called their correlation. The... 

How ever, more often than not, the data is compiled into graphs. Graphs help scientists visualize and interpret the variation in data. Depending on the nature of the data, there are many types of graphs. Bar graphs, pie charts and line graphs are just a few methods used to pictorially represent numerical data. 

Line graphs are generally used to plot continuous data (measurements associated with a standard scale or continuum). Line graphs allow us to interpolate the values of points not directly measured and allow for inference /prediction of future events. 

Line graphs show data points connected by lines different series are given different line markings (for example, dashed or dotted) or different tick marks. Line graphs are useful when the data points are more important than the transitions between them. They best show ... 

Using the discussion of straight line graphs for which in general ... 

This means that we can use the graphs to predict the shifts in concentration that will occur as the system adjusts itself to equilibrium. Thus if one starts at a particular point (say X) which corresponds to a non-equilibrium concentration ratio of A(g)/c° and B(g)/c° then by drawing a line at 45° to the axes (assuming the scale divisions on both axes are identical) from the point until the line intersects the equilibrium line (i.e. Qc/co = Kc/co = 3.0) (at point Y) then the coordinates of the intersection point, Y, will correspond to the final concentration ratios of A(g)/c° and B(g)/c° to be found once equilibrium has been established. 

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