Straight Lines/Standard Curves

TOC

Learning Outcomes

After completing this module you should be able to:

• Describe the linear relationships between two parameters
• Construct and use a standard curve for determining the concentration of a unknown solution using spectroscopy
• Use Beer’s Law and the gradient of a standard curve to determine the concentration of an unknown solution using spectroscopy

Line graphs show trends or relationships between one or more variables in experiments involving numbers.  They allow us to immediately determine the effect of changing one of these numerical variables on another numerical variable you can measure. Though this sounds complicated don’t panic, because you have come across this before.

For example, on the “The Biggest Loser” TV show, it would be interesting to show the rate of weight loss of contestants.   This could be easily displayed by plotting the weight loss of the contestants at the various “weigh ins”.  As all the data collected is numerical (i.e., time, since starting the show and weight) a line graph could be used to show the differences in the rate of weight loss between contestants.   

As the show’s producers decide when the "weigh ins” are going to happen, time is known as the "independent variable".  That is, the variable that the experimenter controls.  The weight of the contestant is dependent on what day is chosen so is known as the "dependent variable".  Convention says that we plot the independent variable (in this case, time) on the bottom or “x-axis” and the person’s weight loss on the “y-axis” (dependent variable). 

Ok now, we have all been on diets.  I personally would want my graph of weight loss to be as steep as possible and never flattening out until my goal weight, but of course this does not happen.  Line graphs can therefore show when a person is losing weight quickly (fast rate) and when they are plateauing (zero rate).   Line graphs are used because it is very easy to interpret rates of change between variables.

As you are now aware, line graphs are not always straight lines.  If you do collect data points that allow you to draw a straight line, you can say there is a correlation between the two variables or a linear relationship.  In science, there are lots of linear relationships–for example, the length of the femur (a leg bone) vs the height of humans, or the excretion of Vitamin B2 in urine vs dose, etc.  In biology, often the first time you deal with linear graphs is using spectroscopy; at low concentrations of chemicals, there is a linear relationship between the absorbance of light through a solution and its concentration.