### 7.1 Linear Patterns

• Math Help

On page 306, you learned that when one variable is a constant multiple of another variable, the pattern with the two variables is proportional. If you take a more advanced course in mathematics, you might see different words used, such as the two variables are "directly proportional" or "show direct variation." You might also see an equation, such as where k is a nonzero number called the constant of proportionality. This equation can be read as "y is directly proportional to x." While you don't need to know how to write this equation for this text, one advantage of writing an equation is using it to make a table of values. For instance, in Example 5, you discovered the pattern "the distance the spring stretches is 3/2 times the weight in pounds." So, the constant of proportionality is k = 3/2 and you can write the equation Using this equation, you can create the table below. • Consumer Suggestion

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• Checkpoint Solution
1. Elasticity is the tendency of a material to return to its original shape. This spring is more elastic since the same weight causes it to stretch less.
2. You can see that the distance in inches the spring stretches is 3/4 times the weight in pounds. So if the weight is 7 pounds, the distance stretched is inches.

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``` ______     ______    _  __    ______    _  __
|      \\  /_   _//  | |/ //  /_   _//  | |/ //
|  --  //   -| ||-   | ' //    -| ||-   | ' //
|  --  \\   _| ||_   | . \\    _| ||_   | . \\
|______//  /_____//  |_|\_\\  /_____//  |_|\_\\
`------`   `-----`   `-` --`  `-----`   `-` --`

``` 