Worksheet: Slope and a Rate of Change

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 𝑦 = 1 3 π‘₯ βˆ’ 5
  • B 𝑦 = 2 3 π‘₯ βˆ’ 5
  • C 𝑦 = 1 4 π‘₯ βˆ’ 5
  • D 𝑦 = βˆ’ π‘₯ βˆ’ 5
  • E 𝑦 = 2 7 π‘₯ βˆ’ 5

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.

Q4:

Find the rate of change for the following graph.

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)

π‘₯ 9 3 βˆ’ 3 βˆ’ 9
𝑦 2 βˆ’ 2 βˆ’ 6 βˆ’ 1 0

(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 βƒ–     βƒ— 𝐴 𝐡 , βƒ–     βƒ— 𝐡 𝐢 , and βƒ–     βƒ— 𝐢 𝐷 .

  • A The slope of βƒ–     βƒ— 𝐴 𝐡 is 10, the slope of βƒ–     βƒ— 𝐡 𝐢 is 1, and the slope of βƒ–     βƒ— 𝐢 𝐷 is βˆ’ 1 0 .
  • B The slope of βƒ–     βƒ— 𝐴 𝐡 is 1 1 0 , the slope of βƒ–     βƒ— 𝐡 𝐢 is 0, and the slope of βƒ–     βƒ— 𝐢 𝐷 is βˆ’ 1 1 0 .
  • C The slope of βƒ–     βƒ— 𝐴 𝐡 is 1 1 0 , the slope of βƒ–     βƒ— 𝐡 𝐢 is 1, and the slope of βƒ–     βƒ— 𝐢 𝐷 is βˆ’ 1 1 0 .
  • D The slope of βƒ–     βƒ— 𝐴 𝐡 is 10, the slope of βƒ–     βƒ— 𝐡 𝐢 is 0, and the slope of βƒ–     βƒ— 𝐢 𝐷 is βˆ’ 1 0 .
  • E The slope of βƒ–     βƒ— 𝐴 𝐡 is 10, the slope of βƒ–     βƒ— 𝐡 𝐢 is undefined, and the slope of βƒ–     βƒ— 𝐢 𝐷 is βˆ’ 1 0 .

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: 1 3 km/h
  • Bfastest speed: 6 km/h, slowest speed: βˆ’ 1 3 km/h
  • Cfastest speed: 3 km/h, slowest speed: 1 6 km/h
  • D fastest speed: 6 km/h, slowest speed: 1 3 km/h
  • Efastest speed: βˆ’ 6 km/h, slowest speed: βˆ’ 1 3 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 𝑦 = 3 1 . 8 + 0 . 4 3 π‘₯ , where π‘₯ is the score in math and 𝑦 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.

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