# Lesson 4

Interpret This, Interpret That

- Let’s explore linear models

### 4.1: Math Talk: Units

Mentally calculate each value.

5 granola bars cost $20. How much is 1 worth?

A car travels at a constant speed and goes 100 miles in 2.5 hours. How fast is the car travelling in miles per hour?

Tyler can do 50 sit-ups in 4 minutes. What is his average sit-ups per minute?

3 ounces of yeast flakes costs $4.29. What is the cost for 1 ounce?

### 4.2: Absences and Scores

Here are a table and scatter plot representing the number of students’ absences and their final exam scores.

student | number of absences | final exam score |
---|---|---|

A | 1 | 94 |

B | 5 | 71 |

C | 1 | 98 |

D | 5 | 70 |

E | 3 | 67 |

F | 2 | 94 |

G | 6 | 71 |

H | 4 | 89 |

I | 5 | 77 |

J | 0 | 90 |

K | 2 | 91 |

L | 11 | 60 |

student | number of absences | final exam score |
---|---|---|

M | 7 | 68 |

N | 8 | 65 |

O | 20 | 42 |

P | 10 | 63 |

Q | 11 | 63 |

R | 20 | 50 |

S | 15 | 67 |

T | 16 | 40 |

U | 4 | 86 |

V | 8 | 82 |

W |

- What are the coordinates of the point in the scatter plot that represents student \(G\)?
- What are the coordinates of the point in the scatter plot that represents student \(R\)?
- What is the final exam score of the student who has perfect attendance?
- What are the final exam scores of the students with the most absences?
- How many absences does the student with the highest score have?
- How many absences does the student with the lowest score have?
- If student \(W\) has 12 absences, what final exam score do you estimate the student will have? Plot this point on the scatter plot.

### 4.3: Elevator Weights

Here is a linear model of the weight of an elevator and the number of people on the elevator.

- Find these values. Explain your reasoning.
- the weight of the elevator when 6 people are on it
- the number of people on the elevator when it weighs 1,400 kg
- the weight of the elevator when no people are on it
- the increase in elevator weight for each additional person according to the model

- Which of your answers corresponds to the slope of the line in the graph?
- Which of your answers corresponds to the \(y\)-intercept of the line in the graph?
- This model can be represented with the equation \(y = 1,\!200 + 50x\). An equation for a different model is written \(y = 70x + 1,\!000\). What are some things you can say about this new model?