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Slope and Rate of Change Practice Tests

These Grade 8 Math practice tests cover slope, rise and run, the slope formula, tables, graphs, slope-intercept form, positive and negative rates, units, and real-world applications.

Skills covered

  • Calculating slope from two points, a graph, a table, or an equation
  • Interpreting positive, negative, zero, and undefined slope
  • Connecting slope with unit rates, output per input, and meaningful units
  • Using \(m=\\frac{\\Delta y}{\\Delta x}\\) and \(y=mx+b\)
  • Modeling travel, cost, data usage, savings, population, altitude, and other changing quantities

How to use these practice tests

Find the change in y and the change in x, divide in the same order, and include the correct sign and units. Then explain what the rate means in the situation.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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5. Test

Grade 8 Slope and Rate of Change Practice Tests

Practice Grade 8 Math questions about slope, rise and run, rate of change, tables, graphs, equations, units, and real-world applications.

Choose the best answer for each question. Include signs and units when interpreting a slope or rate of change.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A bike travels 24 miles in 2 hours at a constant rate. What is the rate?

Please select an answer first.

Correct answer: A

The correct answer is 1212 miles per hour.

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: Divide distance by time: 24div2=1224\\div2=12 miles per hour.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Divide distance by time: 24div2=1224\\div2=12 miles per hour.

2. QuestionMultiple choice

A data plan uses 6 gigabytes over 3 months at a constant rate. What is the rate?

Please select an answer first.

Correct answer: B

The correct answer is 22 gigabytes per month.

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: Divide data by time: 6div3=26\\div3=2 gigabytes per month.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Divide data by time: 6div3=26\\div3=2 gigabytes per month.

3. QuestionMultiple choice

Savings increase from $40 to $100 over 5 weeks. What is the average rate of change?

Please select an answer first.

Correct answer: C

The correct answer is $12 per week.

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: The change is $60 over 5 weeks, so 60div5=1260\\div5=12 dollars per week.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The change is $60 over 5 weeks, so 60div5=1260\\div5=12 dollars per week.

4. QuestionMultiple choice

An elevator descends 900 feet in 3 minutes. What is its average rate of change in altitude?

Please select an answer first.

Correct answer: D

The correct answer is −300-300 feet per minute.

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: Altitude decreases, so the rate is negative: −900div3=−300-900\\div3=-300 feet per minute.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Altitude decreases, so the rate is negative: −900div3=−300-900\\div3=-300 feet per minute.

5. QuestionMultiple choice

Plan A charges $20 plus $0.05 per text. What does the coefficient $0.05 represent?

Please select an answer first.

Correct answer: A

The correct answer is $0.05 per text.

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: In the cost equation C=0.05t+20C=0.05t+20, the coefficient of the input t is the rate per text.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

In the cost equation C=0.05t+20C=0.05t+20, the coefficient of the input t is the rate per text.

6. QuestionMultiple choice

A line passes through (2,7)(2,7) and (6,19)(6,19). What is its rate of change?

Please select an answer first.

Correct answer: B

The correct answer is 33 output units per input unit.

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: m=frac19−76−2=frac124=3m=\\frac{19-7}{6-2}=\\frac{12}{4}=3.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

m=frac19−76−2=frac124=3m=\\frac{19-7}{6-2}=\\frac{12}{4}=3.

7. QuestionMultiple choice

A town population grows from 2,400 to 2,520 in 4 years. What is the average rate of change?

Please select an answer first.

Correct answer: C

The correct answer is 30 people per year.

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: The population change is 120 over 4 years, so 120div4=30120\\div4=30 people per year.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The population change is 120 over 4 years, so 120div4=30120\\div4=30 people per year.

8. QuestionMultiple choice

A negative slope in a distance-versus-time graph can indicate what?

Please select an answer first.

Correct answer: D

The correct answer is The measured distance or position is decreasing as time increases..

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: A negative rate means the output decreases as the input increases; the exact interpretation depends on what the output measures.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

A negative rate means the output decreases as the input increases; the exact interpretation depends on what the output measures.

9. QuestionMultiple choice

Which plan has the greater usage rate: $15 plus $0.08 per unit or $22 plus $0.05 per unit?

Please select an answer first.

Correct answer: A

The correct answer is The first plan, with a rate of $0.08 per unit.

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: The usage rate is the coefficient of the number of units, so $0.08 is greater than $0.05.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The usage rate is the coefficient of the number of units, so $0.08 is greater than $0.05.

10. QuestionMultiple choice

What is the most important unit check for a rate of change?

Please select an answer first.

Correct answer: B

The correct answer is The units should be output units divided by input units..

  1. Identify the two changes: Find the change in the output value and the change in the input value, including their signs and units.
  2. Calculate the rate: A rate of change describes how much the output changes for each unit of input, so its units are output per input.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

A rate of change describes how much the output changes for each unit of input, so its units are output per input.

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