Causal relationships are connections between two things where the state of one changes or affects the state of the other. A causal relationship indicates a correlation between two values, where one actually causes the other to change. In algebra, understanding the relationship between two values can help you predict future values when graphing.
A relationship between two values does not necessarily imply causality. For example, crime rates may go up when populations rise, implying a correlation, but this does not mean that the increase in population caused the crime. However, if temperatures go up outside a house, it will cost more to keep a house cool. The outside temperature directly affects the inside temperature, causing the air conditioner to run more often to maintain a lower inside temperature, and cause the bill for the electricity to increase. So, in this example, if A represents the outside temperature and C is the charge on the bill, as A increases, so must C.
Equations and Causation
Once you know that an increase in temperature will increase the electricity cost, you can see how A affects C and predict future costs based on values of A. For example, if you discover that for every degree the temperature rises (represented by D), the electricity cost goes up $20, you can use an equation to calculate costs. If the temperature is 90 and the bill is $130, when the temperature is 95, you can determine that in this case, D equals five, so C equals $100. Assuming these values remain constant, you will see that graphed values are linear -- when you place the values on a graph, they form points along the same line.
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Other factors also can cause the increase in cost of electricity, such as if people watch more television, wash more clothes or leave more lights on. While temperature-to-cost may be a causal relationship, the watts of electricity used and the cost represents a more direct causal relationship -- the method electricity providers use to determine how much to charge. So, if the company charges 25 cents per watt and you use 20,000 watts in the billing period, your bill would be $5,000.
Algebra tests often give options and ask students to determine whether a relationship is causal or not. Examples of such relationships include the radius of a circle and its area, the number of classes taught and teachers employed, the distance traveled and the time spent traveling or any relationship where the first value directly causes the second.