In this worksheet, we will practice interpreting the slope of a straight line as the rate of change of two quantities.

**Q1: **

Which of the following functions has a rate of change that is more rapid than the function shown in the graph?

- A
- B
- C
- D
- E

**Q2: **

Determine which of the given functions has the greatest rate of change.

(a)

0 | 1 | 2 | |||

2 | 6 | 10 | 14 |

(b) a function where the input is multiplied by 3 and subtracted from 4

(c)

(d)

- Ac
- Bb
- Cd
- Da
- EThey have the same rate of change.

**Q3: **

At an amusement park, a booth was selling soft drinks. By 2:00 pm, 37 soft drinks were sold, and, by 4:00 pm, 69 were sold. Assuming that the booth was selling at a linear rate during this period, determine the slope of the line representing this information.

**Q5: **

Jennifer and Hannah are playing a video game. The given functions represent the number of levels each of them has finished. Who plays better?

Hannah’s Progress | |
---|---|

Time (min) | Number of Levels |

4 | 3 |

36 | 9 |

100 | 15 |

144 | 18 |

- AJennifer
- BHannah

**Q6: **

Which of the following functions has a lower rate of change?

(a)

9 | 3 | |||

2 |

(b) A function with an output that is equal to the input divided by 3 and added to 5.

- AThey have the same rate of change.
- B(a)
- C(b)

**Q7: **

Find the slopes of , , and .

- A The slope of is 10, the slope of is 1, and the slope of is .
- B The slope of is , the slope of is 0, and the slope of is .
- C The slope of is , the slope of is 1, and the slope of is .
- D The slope of is 10, the slope of is 0, and the slope of is .
- E The slope of is 10, the slope of is undefined, and the slope of is .

**Q8: **

Which of the following best describes the slope of the line on the diagram?

- Aundefined
- Bpositive
- C0
- Dnegative

**Q9: **

The graph shows the distance covered in kilometers over a 15-hour hike. What were the fastest and slowest speeds recorded?

- Afastest speed: 3 km/h, slowest speed: km/h
- Bfastest speed: 6 km/h, slowest speed: km/h
- Cfastest speed: 3 km/h, slowest speed: km/h
- D fastest speed: 6 km/h, slowest speed: km/h
- Efastest speed: km/h, slowest speed: km/h

**Q10: **

Use the graph to find out how many action figures each boy has.

**Q11: **

The scores of a class of students in their end-of-year math and physics examinations can be described by the model , where is the score in math and is the score in physics. What is the interpretation of the value of 0.43 in the model?

- AFor every additional point scored in the math examination, students’ scores decrease by, on average, 0.43 points in their physics examination.
- BFor every additional point scored in the physics examination, students’ scores increase by, on average, 0.43 additional points in their math examination.
- CFor every additional point scored in the physics examination, students’ scores decrease by, on average, 0.43 points in their math examination.
- DFor every additional point scored in the math examination, students’ scores increase by, on average, 0.43 additional points in their physics examination.
- EFor every additional point scored in the math examination, students’ scores increase by, on average, 31.8 points in their physics examination.