Lesson Worksheet: Slope and Rate of Change Mathematics • 8th Grade

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?

  • A𝑦=14π‘₯βˆ’5
  • B𝑦=27π‘₯βˆ’5
  • C𝑦=13π‘₯βˆ’5
  • D𝑦=23π‘₯βˆ’5
  • E𝑦=βˆ’π‘₯βˆ’5

Q2:

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

(a)

π‘₯βˆ’2βˆ’1012
π‘¦βˆ’2261014

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

(c)

(d) 𝑦=15π‘₯+8

  • Ac
  • BThey have the same rate of change.
  • Ca
  • Db
  • Ed

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:

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

Scarlett’s Progress
Time (min)Number of Levels
43
129
2015
2418
  • AElizabeth
  • BScarlett

Q6:

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

(a)

π‘₯93βˆ’3βˆ’9
𝑦2βˆ’2βˆ’6βˆ’10

(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(b)
  • C(a)

Q7:

Find the slopes of ⃖⃗𝐴𝐡, ⃖⃗𝐡𝐢, and ⃖⃗𝐢𝐷.

  • AThe slope of ⃖⃗𝐴𝐡 is 10, the slope of ⃖⃗𝐡𝐢 is 0, and the slope of ⃖⃗𝐢𝐷 is βˆ’10.
  • BThe slope of ⃖⃗𝐴𝐡 is 110, the slope of ⃖⃗𝐡𝐢 is 0, and the slope of ⃖⃗𝐢𝐷 is βˆ’110.
  • CThe slope of ⃖⃗𝐴𝐡 is 10, the slope of ⃖⃗𝐡𝐢 is undefined, and the slope of ⃖⃗𝐢𝐷 is βˆ’10.
  • DThe slope of ⃖⃗𝐴𝐡 is 10, the slope of ⃖⃗𝐡𝐢 is 1, and the slope of ⃖⃗𝐢𝐷 is βˆ’10.
  • EThe slope of ⃖⃗𝐴𝐡 is 110, the slope of ⃖⃗𝐡𝐢 is 1, and the slope of ⃖⃗𝐢𝐷 is βˆ’110.

Q8:

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

  • Apositive
  • B0
  • Cnegative
  • Dundefined

Q9:

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

  • AFastest speed: βˆ’6 km/h, slowest speed: βˆ’13 km/h
  • BFastest speed: 6 km/h, slowest speed: βˆ’13 km/h
  • CFastest speed: 3 km/h, slowest speed: 13 km/h
  • DFastest speed: 6 km/h, slowest speed: 13 km/h
  • EFastest speed: 3 km/h, slowest speed: 16 km/h

Q10:

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

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