Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Slope and a Rate of Change

In this lesson, we will learn how to interpret the slope of a straight line as the rate of change of two quantities.

Worksheet • 11 Questions

Q1:

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)

  • Aa
  • BThey have the same rate of change.
  • Cb
  • Dd
  • Ec

Q2:

Find the rate of change for the following graph.

Q3:

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

  • Anegative
  • Bpositive
  • C0
  • Dundefined

Q4:

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

  • A fastest speed: 6 km/h, slowest speed: 1 3 km/h
  • Bfastest speed: − 6 km/h, slowest speed: − 1 3 km/h
  • Cfastest speed: 6 km/h, slowest speed: − 1 3 km/h
  • Dfastest speed: 3 km/h, slowest speed: 1 6 km/h
  • Efastest speed: 3 km/h, slowest speed: 1 3 km/h

Q5:

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

Rania’s Progress
Time (min) Number of Levels
4 3
36 9
100 15
144 18
  • ARania
  • BEngy

Q6:

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.

Q7:

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

  • A 𝑦 = − 𝑥 − 5
  • B 𝑦 = 2 7 𝑥 − 5
  • C 𝑦 = 2 3 𝑥 − 5
  • D 𝑦 = 1 4 𝑥 − 5
  • E 𝑦 = 1 3 𝑥 − 5

Q8:

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

Q9:

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

(a)

𝑥 9 3 − 3 − 9
𝑦 2 − 2 − 6 − 1 0

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

  • A(a)
  • B(b)
  • CThey have the same rate of change.

Q10:

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

Q11:

Find the slopes of ⃖ ⃗ 𝐴 𝐵 , ⃖ ⃗ 𝐵 𝐶 , and ⃖ ⃗ 𝐶 𝐷 .

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

Related Lessons