# Linear Functions Worksheet

### Solutions

#### Represent Each Equation Graphically:

1 y = 2

2y = −2

3 y = ¾

4y = 0

5x = 0

6 x = − 5

7y = x

8y = 2x

9y = 2x − 1

10y = −2x − 1

11y = ½x − 1

12y = ½x − 1

13Graph the following functions based on the information given:

1 The line has a slope of −3 and its y-intercept is −1.

2 The line has a slope of 4 and passes through the point (−3, 2).

3 The line passes through points A (−1, 5) and B (3, 7).

4 The line passes through point P (2, −3) and is parallel to the line y = −x + 7.

## 1

y = 2 is a constant function.

## 2

y = −2 is a constant function.

## 3

y = ¾ is a constant function.

## 4

y = 0 is a constant function.

## 5

x = 0 is a vertical line.

## 6

x = −5 is a vertical line.

## 7

y = x is the identity function.

x | y = x |
---|---|

0 | 0 |

1 | 1 |

## 8

y = 2x is a linear function.

x | f(x) = 2x |
---|---|

0 | 0 |

1 | 2 |

## 9

y = 2x − 1 is a linear function.

x | y = 2x − 1 |
---|---|

0 | −1 |

1 | 1 |

## 10

y = −2x − 1 is a linear function.

x | y = −2x − 1 |
---|---|

0 | −1 |

1 | −3 |

## 11

y = ½x − 1 is a linear function.

x | y = ½x − 1 |
---|---|

0 | −1 |

2 | 0 |

## 12

y = −¾x − 1 is a linear function.

x | y = −¾x − 1 |
---|---|

0 | −1 |

4 | −4 |

## 13

Graph the following functions based on the information given:

1 The line has a slope of −3 and its y-intercept is −1.

**y = −3x −1**

x | y = −3x − 1 |
---|---|

0 | −1 |

1 | −4 |

2 The line has a slope of 4 and passes through the point (−3, 2).

y = 4 x + b 2 = 4 · (−3) +b b = 14

y = 4 x + 14

x | y = 4x +14 |
---|---|

0 | 14 |

1 | 18 |

3 The line passes through points A (−1, 5) and B (3, 7).

5 = −m + b −5 = m − b

7 = 3m + b 7 = 3m + b

2 = 4m m = ½ b = 11/2

**y= ½x + 11/2**

x | y = ½x + 11/2 |
---|---|

0 | −1 |

1 | −2 |

4 The line passes through point P (2, −3) and is parallel to the line y = −x + 7.

m = −1

−3 = − 1 · (−2) + b b = − 1

**y = −x −1**

x | y = −x −1 |
---|---|

0 | −1 |

1 | −2 |