Algebraic Rule: Definition & Concept

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• 0:00 What Are Algebraic Rules?
• 1:02 Creating Your Own Rule
• 1:42 Examples
• 3:44 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
An algebraic rule is a method for describing the relationship between two variables. This lesson will give a definition of an algebraic rule, show some examples and give you the steps to create rules when given a set of data.

What Are Algebraic Rules?

Frequently, in life, it seems like there are rules on top of rules for just about everything. And although it may seem frustrating at times, the rules are there for a reason and generally make everyone's life better.

The same is true with algebraic rules. There may seem like a lot of them, but they are extremely helpful when trying to solve problems. The main purpose of algebraic rules is to make sense of sets of data involving two or more variables.

For example, the equation d = rt is an algebraic rule.

d = distance

r = rate

t = time

This rule gives the relationship between distance, rate and time. If you know that your car can average 50 mph for the trip from your house to the mall, which is 75 miles away, you can figure out how long it will take you to get there.

75 miles = (50mph)(t)

Divide both sides by 50 to isolate t

t = 1.5 hours

There are as many algebraic rules as there are problems to be solved. Many of them are standardized for certain types of problems, such as the distance problem or formulas for finding the area or volume of certain shapes. There are also ways to come up with your own algebraic rules to fit any scenario. Take the following chart:

To write the algebraic rule that fits these numbers, we first have to figure out the pattern that is created. Each y-value is twice that of its corresponding x-value. Therefore, the rule of these numbers is:

y = 2x

Once we know this, we can determine the y-value that goes along with any x-value. If x is 200, we know that y will be 400.

Examples

1.) Write an algebraic rule from the data given in the following table:

Sometimes, when the rule you are trying to write is not obvious from the data, it is easier to draw a graph of the data and then write the rule from there.

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