TOPIC

Representing patterns in linear relations

MY PROGRESS

Pug Score

0%

Best Streak

0 in a row

Study Points

+0

Overview

Practice

Watch

Read

Quiz

Next Steps

Get Started

Get unlimited access to all videos, practice problems, and study tools.

Try Now
Unlimited practice
Full videos

Back to Menu

Topic Progress

Pug Score

0%

Videos Watched

0/0

Best Practice

No score

Read

Not viewed

Best Quiz

No attempts

Best Streak

0 in a row

Study Points

+0

Read

Representing Patterns in Linear Relations

A growing pattern that adds the same amount at each step can be written as a linear rule: a starting value plus a constant times the term number. Learn to find that rule from a picture pattern, see a worked squares example, and understand why plotting the pattern gives a straight line.

Representing a pattern with a rule

A growing pattern adds the same amount at each step, so it can be described by a linear rule: a starting value plus a constant times the term number.

Worked example

A pattern of squares grows by 3 squares each term: term 1 has 4 squares, term 2 has 7, term 3 has 10, and term 4 has 13. Since each term adds exactly 3, the rule is squares = 3n + 1, where n is the term number.

Representing a growing pattern as a linear rule A pattern grows by 3 squares each term: term 1 has 4 squares, term 2 has 7, term 3 has 10, term 4 has 13. Plotting the number of squares against the term number gives a straight line, because the rule 3n+1 is linear. term (n) squares 471013 rule: squares = 3n + 1
Plotting the pattern's values against the term number gives a straight line, since the rule is linear.

Notice that plotting term number against the number of squares gives points that fall on a straight line — this is exactly what makes a pattern "linear."

Finding the rule from a pattern

To find the rule for any growing pattern: find the constant difference between consecutive terms (that becomes the coefficient of n), then work out what value makes term 1 come out correctly (that becomes the added constant). This turns a picture or a table of values into an equation you can use to predict any term, and is a first step toward linear equations in general.

Related lessons