### Student Page 2.8.4 Distinguishing Linear from Other Functions

#### 1.

What do you know about linear equations? Give brief answers now and think about these questions as you work on the problems below.

##### (a)

What patterns would you see in a table of data that can be modeled by a linear equation?

##### (b)

How can you tell a graph can be modeled by a linear equation?

##### (c)

What does an equation of a linear equation look like?

##### (d)

How can you tell a story can be modeled by a linear equation?

#### 2.

Study the data sets. Label each data set as linear or non-linear. Explain your choice.

##### (a)

\(x\) | \(y\) |
---|---|

\(-5\) | \(-14\) |

\(-4\) | \(-12\) |

\(-3\) | \(-10\) |

\(-2\) | \(-8\) |

\(-1\) | \(-6\) |

0 | \(-4\) |

1 | \(-2\) |

2 | 0 |

3 | 2 |

4 | 4 |

5 | 6 |

Linear / Non-linear? Explain:

##### (b)

\(x\) | \(y\) |
---|---|

\(-5\) | 0.03125 |

\(-4\) | 0.0625 |

\(-3\) | 0.125 |

\(-2\) | 0.25 |

\(-1\) | 0.5 |

0 | 1 |

1 | 2 |

2 | 4 |

3 | 8 |

4 | 16 |

5 | 32 |

Linear / Non-linear? Explain:

##### (c)

\(x\) | \(y\) |
---|---|

\(-5\) | 25 |

\(-4\) | 16 |

\(-3\) | 9 |

\(-2\) | 4 |

\(-1\) | 1 |

0 | 0 |

1 | 1 |

2 | 4 |

3 | 9 |

4 | 16 |

5 | 25 |

Linear / Non-linear? Explain:

#### 3.

Categorize each graph as linear or non-linear. Explain your choice.

##### (a)

Linear / Non-linear? Explain:

##### (b)

Linear / Non-linear? Explain:

##### (c)

Linear / Non-linear? Explain:

#### 4.

Gather data for each story. Label each data set as linear or non-linear. Explain your choice.

##### (a)

Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose grows 3 inches. How long will his nose be after 1 lie? 2 lies? 3 lies? \(L\) lies?

Lie Number | Nose Length in inches |
---|---|

0 | 2 |

1 | |

2 | |

3 | |

4 | |

5 | |

\(L\) |

Linear / Non-linear? Explain:

##### (b)

Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose doubles in length. How long will his nose be after 1 lie? 2 lies? 3 lies? \(L\) lies?

Lie Number | Nose Length in inches |
---|---|

0 | 2 |

1 | |

2 | |

3 | |

4 | |

5 | |

\(L\) |

Linear / Non-linear? Explain:

##### (c)

Geppetto carved Pinocchio a 2-inch long nose. Each time Pinocchio tells a lie, his nose grows from its previous length by the same number of inches as the number of lies he has told. For example, after 1 lie, his nose will be 2 + 1 = 3 inches long. After 2 lies, his nose will be 3 + 2 = 5 inches long. How long will his nose be after 3 lies? 4 lies? 5 lies? \(L\) lies?

Lie Number | Nose Length in inches |
---|---|

0 | 2 |

1 | 3 |

2 | 5 |

3 | |

4 | |

5 | |

\(L\) |

Linear / Non-linear? Explain:

#### 5.

Categorize each equation as linear or non-linear. Explain your choice.

##### (a)

\(y = 3x + 4\)

Linear / Non-linear? Explain:

##### (b)

\(y = 2^x + 3\)

Linear / Non-linear? Explain:

##### (c)

\(y = x^2 + 1\)

Linear / Non-linear? Explain:

#### 6.

Revisit Exercise 2.8.3.1. What can you add to your previous answers? Use more space as needed.

##### (a)

What patterns would you see in a table that can be modeled by a linear equation?

##### (b)

How can you tell a graph can be modeled by a linear equation?

##### (c)

What does an equation of a linear equation look like?

##### (d)

How can you tell a story can be modeled by a linear equation?