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 were 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.

Q11:

The scores of a class of students in their end-of-year math and physics examinations can be described by the model 𝑦=31.8+0.43π‘₯, 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 increase by, on average, 31.8 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 decrease by, on average, 0.43 points in their physics examination.

Q12:

Let 𝑓(π‘₯)=2(3βˆ’π‘₯)(π‘₯+1) and 𝑔 be the quadratic function given by the following table.

π‘₯βˆ’2βˆ’10123
𝑔(π‘₯)030βˆ’9βˆ’24βˆ’45

Which of the following statements is true?

  • AOn the interval 0<π‘₯<3, function 𝑓 has the lower average rate of change.
  • BOn the interval 0≀π‘₯≀3, function 𝑓 has the higher average rate of change.
  • CThe minimum value of 𝑓 is greater than the maximum value of 𝑔.
  • DBoth functions have the same axis of symmetry.
  • EThe sums of zeros of the two functions are the same.

Q13:

The table lists the distance covered in kilometers over a 15-hour hike. During which periods was the average speed below 2 kilometers per hour?

Hour35915
Distance18242830
  • Abetween hour 5 and hour 15
  • Bbetween hour 3 and hour 5

Q14:

Using the information in the given table, determine the rate of change in the number of seeds for every orange, and express your answer as a fraction.

Number of Oranges357
Number of Seeds5490126
  • A121
  • B365
  • C112
  • D118
  • E181

Q15:

Which of the following interprets the rate of change of the data in the table?

Remaining Gas (gal)191494
Miles Driven0100200300
  • AA decrease of 19 gallons per 50 miles
  • BA decrease of 19 gallons per 100 miles
  • CA decrease of 5 gallons per 100 miles
  • DA decrease of 5 gallons per 50 miles

Q16:

A video-on-demand service offers different streaming plans as shown in the given table. Determine, to the nearest cent, the rate of change in cost per minute of video streaming.

Cost$42$58$74$90$106
Minutes of Video Streaming5,0005,5006,0006,5007,000

Q17:

The table shows Sophia’s height at ages 10 and 15. Find the rate of change, in inches per year, of her height between these ages.

Height (in)5367
Age (yr)1015
  • A514 inches per year
  • B245 inches per year
  • C5310 inches per year
  • D1567 inches per year
  • E1053 inches per year

Q18:

Using the given table, determine the rate of change in temperature.

Time (in hours)1:00 PM2:00 PM3:00 PM4:00 PM
Temperature (in degrees)55596367
  • A16∘ per hour
  • B29∘ per hour
  • C4∘ per hour
  • D2∘ per hour
  • E28∘ per hour

Q19:

The table shows the value of a company’s stock over a 5-day period. Determine the rate of change (dollars per day) between day 1 and day 3.

Value ($)40.2345.5549.8741.2145.62
Day12345

Q20:

The graph below shows the relation between the cost of a party and the number of people attending. Determine the rate of change.

  • A27512
  • B1758
  • C25
  • D475
  • E754

Q21:

The relation between the cost of wrapping paper and the number of rolls bought is shown in the table. Is the relationship between the two quantities linear? If so, find the constant rate of change.

Number of Rolls1234
Total Cost ($)37912
  • AYes, 3
  • BYes, βˆ’4
  • CYes, βˆ’3
  • DNo
  • EYes, 4

Q22:

What is the average speed of a sound wave that travels 895 meters in 2.5 seconds?

Q23:

If a worker who can paint a house in 300 hours and another who can paint the same house in 100 hours work together, how many minutes do they need to paint the house?

Q24:

Given the exponential function 𝑦=4(1.21)οŠ±ο—, what is the percentage rate of change? Give your answer to the nearest percent.

Q25:

At 5:00, the water level in a pool reaches a height of 10 inches. At 8:00, the water level is at 50 inches. What is the rate of change of the water level per minute?

  • A59 of an inch per minute
  • B403Β of an inch per minute
  • C340Β of an inch per minute
  • D29Β of an inch per minute
  • E92Β of an inch per minute

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