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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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1. 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

What is the slope of the line through (1,2)(1,2) and (3,6)(3,6)?

Please select an answer first.

Correct answer: A

The correct answer is 22.

  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=fracy2−y1x2−x1=frac6−23−1=frac42=2m=\\frac{y_2-y_1}{x_2-x_1}=\\frac{6-2}{3-1}=\\frac{4}{2}=2.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Use m=fracy2−y1x2−x1=frac6−23−1=frac42=2m=\\frac{y_2-y_1}{x_2-x_1}=\\frac{6-2}{3-1}=\\frac{4}{2}=2.

2. QuestionMultiple choice

What is the slope of the line through (−2,4)(-2,4) and (2,12)(2,12)?

Please select an answer first.

Correct answer: B

The correct answer is 22.

  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 slope is m=frac12−42−(−2)=frac84=2m=\\frac{12-4}{2-(-2)}=\\frac{8}{4}=2.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The slope is m=frac12−42−(−2)=frac84=2m=\\frac{12-4}{2-(-2)}=\\frac{8}{4}=2.

3. QuestionMultiple choice

What is the slope of the line through (0,5)(0,5) and (4,1)(4,1)?

Please select an answer first.

Correct answer: C

The correct answer is −1-1.

  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: Calculate m=frac1−54−0=frac−44=−1m=\\frac{1-5}{4-0}=\\frac{-4}{4}=-1.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Calculate m=frac1−54−0=frac−44=−1m=\\frac{1-5}{4-0}=\\frac{-4}{4}=-1.

4. QuestionMultiple choice

What is the slope of the line through (3,−2)(3,-2) and (3,7)(3,7)?

Please select an answer first.

Correct answer: D

The correct answer is Undefined.

  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 x-values are equal, so Deltax=0\\Delta x=0. Division by zero makes the slope undefined, which describes a vertical line.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The x-values are equal, so Deltax=0\\Delta x=0. Division by zero makes the slope undefined, which describes a vertical line.

5. QuestionMultiple choice

What is the slope of the line through (−1,4)(-1,4) and (3,4)(3,4)?

Please select an answer first.

Correct answer: A

The correct answer is 00.

  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 y-values do not change, so Deltay=0\\Delta y=0 and m=0m=0.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The y-values do not change, so Deltay=0\\Delta y=0 and m=0m=0.

6. QuestionMultiple choice

Which formula gives the slope between two points?

Please select an answer first.

Correct answer: B

The correct answer is m=fracy2−y1x2−x1m=\\frac{y_2-y_1}{x_2-x_1}.

  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: Slope is the change in output divided by the change in input: m=fracDeltayDeltax=fracy2−y1x2−x1m=\\frac{\\Delta y}{\\Delta x}=\\frac{y_2-y_1}{x_2-x_1}.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Slope is the change in output divided by the change in input: m=fracDeltayDeltax=fracy2−y1x2−x1m=\\frac{\\Delta y}{\\Delta x}=\\frac{y_2-y_1}{x_2-x_1}.

7. QuestionMultiple choice

What is the slope of the line through (2,1)(2,1) and (6,9)(6,9)?

Please select an answer first.

Correct answer: C

The correct answer is 22.

  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=frac9−16−2=frac84=2m=\\frac{9-1}{6-2}=\\frac{8}{4}=2.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

m=frac9−16−2=frac84=2m=\\frac{9-1}{6-2}=\\frac{8}{4}=2.

8. QuestionMultiple choice

What is the slope of the line through (−4,6)(-4,6) and (2,−6)(2,-6)?

Please select an answer first.

Correct answer: D

The correct answer is −2-2.

  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=frac−6−62−(−4)=frac−126=−2m=\\frac{-6-6}{2-(-4)}=\\frac{-12}{6}=-2.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

m=frac−6−62−(−4)=frac−126=−2m=\\frac{-6-6}{2-(-4)}=\\frac{-12}{6}=-2.

9. QuestionMultiple choice

A line rises from left to right. What sign does its slope have?

Please select an answer first.

Correct answer: A

The correct answer is Positive.

  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: When y increases as x increases, Deltay\\Delta y is positive while Deltax\\Delta x is positive, so the slope is positive.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

When y increases as x increases, Deltay\\Delta y is positive while Deltax\\Delta x is positive, so the slope is positive.

10. QuestionMultiple choice

What are the units of a rate of change when the output is measured in dollars and the input is measured in hours?

Please select an answer first.

Correct answer: B

The correct answer is Dollars 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: Rate of change is output units per input unit, so the units are dollars per hour.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Rate of change is output units per input unit, so the units are dollars per hour.

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