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Name
4-2
Class
Date
Enrichment
Patterns and Linear Functions
Representing Number Patterns With Linear Equations
Many number patterns can be represented by a linear equation. For example, the
positive even integers, 2, 4, 6, 8, . . . , can be represented by the equation y = 2x,
where x represents the position in the sequence. The fourth even integer (x = 4) is y
= 2(4) or 8. If you can determine an equation to describe the number pattern, you
can use the equation to determine the value of any number in the pattern. For
example, the 300th positive even integer is y = 2(300) or 600. Using the equation
makes determining the values faster and easier than writing out the entire list.
Exercises
1. Write a linear equation to describe the number pattern 3, 6, 9, . . .
2. Write a linear equation to describe the number pattern 0, 5, 10, 15, . . .
3. Write a linear equation to describe the number pattern 4, 7, 10, . . .
4. Write a linear equation to describe the number pattern that starts with 8 and
continues with numbers that are one more than a positive multiple of 7.
5. Write a linear equation to describe the number pattern that starts with 3 and
continues with positive odd integers.
6. Write a linear equation to describe the number pattern that starts with –2 and
continues with negative even integers.
7. Write a linear equation to describe the number pattern that starts with –8 and
continues with negative multiples of 8.
8. Open-Ended Write a number pattern of your own. Can you write a linear
equation to describe the pattern? If so, write the equation. If you cannot
determine a linear equation for the pattern, write a new pattern for which
you can write a linear equation.
Prentice Hall Algebra 1 • Teaching Resources
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