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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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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

Three notebooks cost $12 total at a constant rate. What is the unit rate?

Please select an answer first.

Correct answer: A

The correct answer is $4 per notebook.

  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 the total cost by the number of notebooks: 12div3=412\\div3=4 dollars per notebook.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Divide the total cost by the number of notebooks: 12div3=412\\div3=4 dollars per notebook.

2. QuestionMultiple choice

A car travels 180 miles in 3 hours at a constant speed. What is the rate?

Please select an answer first.

Correct answer: B

The correct answer is 6060 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: The rate is distance divided by time: 180div3=60180\\div3=60 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.

The rate is distance divided by time: 180div3=60180\\div3=60 miles per hour.

3. QuestionMultiple choice

A tank fills with 48 gallons in 6 minutes. What is the rate?

Please select an answer first.

Correct answer: C

The correct answer is 88 gallons 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: Divide gallons by minutes: 48div6=848\\div6=8 gallons per minute.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Divide gallons by minutes: 48div6=848\\div6=8 gallons per minute.

4. QuestionMultiple choice

A temperature rises 15 degrees over 5 hours. What is the average rate of change?

Please select an answer first.

Correct answer: D

The correct answer is 33 degrees 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: The average rate is frac155=3\\frac{15}{5}=3 degrees per hour.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The average rate is frac155=3\\frac{15}{5}=3 degrees per hour.

5. QuestionMultiple choice

Five pounds of fruit cost $17.50. What is the unit price?

Please select an answer first.

Correct answer: A

The correct answer is $3.50 per pound.

  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 the cost by the weight: 17.50div5=3.5017.50\\div5=3.50 dollars per pound.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Divide the cost by the weight: 17.50div5=3.5017.50\\div5=3.50 dollars per pound.

6. QuestionMultiple choice

A runner travels 2.4 kilometers in 0.3 hours. What is the rate?

Please select an answer first.

Correct answer: B

The correct answer is 88 kilometers 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: 2.4div0.3=82.4\\div0.3=8 kilometers 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: 2.4div0.3=82.4\\div0.3=8 kilometers per hour.

7. QuestionMultiple choice

An employee earns $50 plus $12 for each hour worked. What is the rate of change of earnings?

Please select an answer first.

Correct answer: C

The correct answer is $12 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: In E=12h+50E=12h+50, the coefficient of h is 12 dollars per hour; 50 is the starting value.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

In E=12h+50E=12h+50, the coefficient of h is 12 dollars per hour; 50 is the starting value.

8. QuestionMultiple choice

A water level decreases by 4 liters each minute. What is the rate of change?

Please select an answer first.

Correct answer: D

The correct answer is −4-4 liters 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: Because the amount decreases, the change is negative: m=−4m=-4 liters per minute.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Because the amount decreases, the change is negative: m=−4m=-4 liters per minute.

9. QuestionMultiple choice

Which rate is greater: 45 miles in 5 hours or 32 miles in 4 hours?

Please select an answer first.

Correct answer: A

The correct answer is 45div5=945\\div5=9 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: The rates are 9 miles per hour and 8 miles per hour, so 9 miles per hour is greater.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The rates are 9 miles per hour and 8 miles per hour, so 9 miles per hour is greater.

10. QuestionMultiple choice

A quantity changes from 18 to 30 while the input changes from 2 to 5. What is the rate of change?

Please select an answer first.

Correct answer: B

The correct answer is 44 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: Use m=frac30−185−2=frac123=4m=\\frac{30-18}{5-2}=\\frac{12}{3}=4 units per input unit.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Use m=frac30−185−2=frac123=4m=\\frac{30-18}{5-2}=\\frac{12}{3}=4 units per input unit.

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