Dependent and Independent Variables

If you are a student studying precalculus, physics or chemistry, you are no doubt memorizing the definitions of independent and dependent variables.  So what do they mean?

Experiments are devised so that you change something and record the response.  The variable that you are changing, whether its the concentration of substrate, time, an increase in temperature, etc., is your independent variable.  I like to think of an independent variable as your “input.”  Your result, or response to this change, becomes your dependent variable or your “output”.

Let’s take a look at the following experiment.  Last night, I made pumpkin cookies.  I made 3 batches.  One batch had 1 cup of flour, the second batch used 2 cups of flour, and the third batch used three cups of flour.  In the first batch, I made 12 cookies, the second batch I made 24 cookies and the third batch I made 36 cookies.  What is the independent and dependent variable in this experiment?

The independent variable is the cups of flour.  I input different amounts of flour into the recipe.  It’s the only variable I am changing.  My result (the output) is how many cookies I was able to make with each batch.  So the number of cookies is my dependent variable.  The number of cookies is dependent on the amount of flour I used in the recipe.

We can graph this experiment on an X-Y coordinate plan.  The x-axis is labeled with the independent variable and the y-axis is labeled with the dependent variable.  This way we can see that the number of cookies is directly proportional to the amount of flour.

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