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Comparing Rates of Change - Printable Mathematics Worksheets grade 8 - Wayground

Comparing Rates of Change

10 questions

8th - 8th Grade

Mathematics

Comparing Rates of Change is a Grade 8 mathematics worksheet that helps students interpret and compare slope across equations, graphs, tables, and real-world situations. Its 10 questions ask students to order rates of change from steepest to least steep, compare values, identify which equations or lines are steeper, match graphs to rates of change, and determine starting elevations and differences between initial values. The worksheet combines one ordering item, one dropdown comparison, five multiple-choice questions, one graph-matching activity, and two math-response problems. Students must distinguish a line’s rate of change from its initial value while using both direction and steepness to compare functions. This free printable worksheet is useful for Grade 8 math practice, review, or a quick check of understanding, and it includes a complete answer key for efficient grading.

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Comparing Rates of Change

Total questions: 10

Name
Class
Date
1.

The following are rates of change for different functions.  Order the rates from steepest to least steep.

∣18∣,∣−6∣,∣9∣,∣−32∣,∣ −45∣\left|18\right|,\left|-6\right|,\left|9\right|,\left|-32\right|,\left|\ -45\right|

a)

∣−45∣\left|-45\right|

b)

∣−32∣\left|-32\right|

c)

∣18∣\left|18\right|

d)

∣9∣\left|9\right|

e)

∣−6∣\left|-6\right|

1)
2)
3)
4)
5)
2.

Compare using >,<, or ≡>,<,\ or\ \equiv .

∣11∣\left|11\right| ​ (a)   ∣−13∣\left|-13\right|

∣−26∣\left|-26\right| ​ ​ (b)   ∣16∣\left|16\right|

​ ∣−95∣\left|-95\right| (c)   ∣95∣\left|95\right|

Choose from the below words

<<  

>>  

==  

3.

Equation A: y=2x+3y=2x+3

Equation B: y=3x−3y=3x-3

Which equation has a steeper slope?

a)

Equation A

b)

Equation B

c)

They have the same slope

d)

This cannot be determined.

4.

Equation A: y=−2x+3y=-2x+3

Equation B: y=2x+7y=2x+7

Which equation has a steeper slope?

a)

Equation A

b)

Equation B

c)

They have the same steepness.

d)

This cannot be determined

5.

A biologist is scuba diving. The graph shows the biologist rising over time.

At what elevation did the biologist start going up?

a)

6.5

b)

-80

c)

6

d)

12.5

6.

A coworker of the biologist is scuba diving. The table shows the coworker's descent in elevation over time.

At what elevation did the coworker start descending?

a)

-20

b)

-76

c)

-132

d)

-188

7.

Which line is the steepest?

a)

Line A

b)

Line B

c)

Line C

d)

Line A and C

8.

Match the graphs to their rate of change.

*Hint: pay attention to direction and steepness*

-7

-3

10

3

9.

Equation A: y=23x+15y=23x+15

Equation B: y=13x+10y=13x+10

What is the difference between the initial values?

10.

Equation A: y=6x+17y=6x+17

Equation B: y=14x+3y=14x+3

What is the difference between the initial values?

Answer Key

Comparing Rates of Change

Total questions: 10

1.
a, b, c, d, e
2.

<<  

,

>>  

,

==  

3.
b)

Equation B

4.
c)

They have the same steepness.

5.
b)

-80

6.
a)

-20

7.
b)

Line B

8.
 - 

-7

,  - 

-3

,  - 

10

,  - 

3

9.

55

10.

1414

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FAQs

What does the Comparing Rates of Change worksheet cover?

This Grade 8 worksheet focuses on comparing rates of change across equations, graphs, tables, and contextual situations. Its 10 items require students to order rates by steepness, identify steeper or equally steep lines and equations, match graphs to rates, read starting elevations, and calculate differences between initial values.

How can I use this worksheet to teach students to compare rates of change?

Introduce the worksheet by reviewing that slope describes both a line’s direction and how steeply it changes, while the initial value identifies where a relationship starts. Have students explain their reasoning as they move from the ordering and equation-comparison items to the graph matching, scuba-diving contexts, and final initial-value responses; ask them to discuss why a steeper line does not necessarily have a larger starting value.

What mistakes should I watch for when students complete this worksheet?

Students may confuse steepness with the initial value, choosing the equation or graph that starts higher instead of the one with the greater rate of change. They may also overlook whether a rate is increasing or decreasing, misread the starting elevation in the scuba-diving items, or match graphs by appearance without considering both direction and steepness.

How do I assign and grade this Comparing Rates of Change worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for the ordering, comparison, matching, multiple-choice, and math-response items. For printable submissions, you can scan student work with the Wayground for Teachers app to support grading.

How can I differentiate this rates-of-change worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the equation, graph, and response items easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while keeping the rates-of-change tasks in the same format.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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