### Student Page 2.7.4 Finding Equations from Representations

Directions: Tables, graphs (use grid points!), and stories are provided. For each case:

Find the slope.

Find the \(y\)-intercept.

Write an equation.

Explain how you know the slope and \(y\)-intercept are correct. Check 2 points in your equation to show it is correct.

#### 1.

##### (a) Linear Function Representation.

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

0 | 4 |

2 | 9 |

4 | 14 |

6 | 19 |

8 | 24 |

##### (b) Slope.

Say how you know you are correct.

##### (c) \(y\)-intercept.

Say how you know you are correct.

##### (d) Equation.

Answer:

#### 2.

##### (a) Linear Function Representation.

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

6 | 11 |

9 | 9 |

12 | 7 |

15 | 5 |

18 | 3 |

##### (b) Slope.

Say how you know you are correct.

##### (c) \(y\)-intercept.

Say how you know you are correct.

##### (d) Equation.

Answer:

#### 3.

##### (a) Linear Function Representation.

##### (b) Slope.

Say how you know you are correct.

##### (c) \(y\)-intercept.

Say how you know you are correct.

##### (d) Equation.

Answer:

#### 4.

##### (a) Linear Function Representation.

##### (b) Slope.

Say how you know you are correct.

##### (c) \(y\)-intercept.

Say how you know you are correct.

##### (d) Equation.

Answer:

#### 5.

##### (a) Linear Function Representation.

Hannah shelters her dog at Happy Trails Kennel while she is out of town. Happy Trails requires Hannah to begin each month with $200 in her account and charges her account $15 each day her dog stays at the kennel. What amount, \(A\text{,}\) will Hannah have in her account at the end of the month if her dog stays at the kennel for \(d\) days?

##### (b) Slope.

Say how you know you are correct.

##### (c) \(y\)-intercept.

Say how you know you are correct.

##### (d) Equation.

Answer:

#### 6.

##### (a) Linear Function Representation.

What is the total cost, \(C\text{,}\) of \(x\) months of use of the Fitness Fun health club? Fitness Fun charges a $75 initiation fee plus $20 per month.

##### (b) Slope.

Say how you know you are correct.

##### (c) \(y\)-intercept.

Say how you know you are correct.

##### (d) Equation.

Answer: