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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

A table has x-values 0,1,20,1,2 and y-values 3,5,73,5,7. What is the rate of change?

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: Each increase of 1 in x produces an increase of 2 in y, so the slope is 2.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Each increase of 1 in x produces an increase of 2 in y, so the slope is 2.

2. QuestionMultiple choice

A table has x-values 1,2,31,2,3 and y-values 10,7,410,7,4. What is the rate of change?

Please select an answer first.

Correct answer: B

The correct answer is −3-3.

  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: For each increase of 1 in x, y decreases by 3, so m=−3m=-3.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

For each increase of 1 in x, y decreases by 3, so m=−3m=-3.

3. QuestionMultiple choice

For the proportional relationship y=4xy=4x, what is the rate of change?

Please select an answer first.

Correct answer: C

The correct answer is 44.

  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 y=mxy=mx, the coefficient of x is the constant rate of change, so m=4m=4.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

In y=mxy=mx, the coefficient of x is the constant rate of change, so m=4m=4.

4. QuestionMultiple choice

A graph rises 6 units for every 3 units it moves right. What is the slope?

Please select an answer first.

Correct answer: D

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=fractextrisetextrun=frac63=2m=\\frac{\\text{rise}}{\\text{run}}=\\frac{6}{3}=2.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

m=fractextrisetextrun=frac63=2m=\\frac{\\text{rise}}{\\text{run}}=\\frac{6}{3}=2.

5. QuestionMultiple choice

What is the slope of the line through (0,−2)(0,-2) and (5,8)(5,8)?

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: m=frac8−(−2)5−0=frac105=2m=\\frac{8-(-2)}{5-0}=\\frac{10}{5}=2.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

m=frac8−(−2)5−0=frac105=2m=\\frac{8-(-2)}{5-0}=\\frac{10}{5}=2.

6. QuestionMultiple choice

What is the slope of y=−0.5x+7y=-0.5x+7?

Please select an answer first.

Correct answer: B

The correct answer is −0.5-0.5.

  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 slope-intercept form y=mx+by=mx+b, the coefficient of x is the slope, so m=−0.5m=-0.5.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

In slope-intercept form y=mx+by=mx+b, the coefficient of x is the slope, so m=−0.5m=-0.5.

7. QuestionMultiple choice

What is the slope of the horizontal line y=4y=4?

Please select an answer first.

Correct answer: C

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: A horizontal line has no vertical change, so Deltay=0\\Delta y=0 and its slope is 0.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

A horizontal line has no vertical change, so Deltay=0\\Delta y=0 and its slope is 0.

8. QuestionMultiple choice

What is the slope of the vertical line x=−2x=-2?

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: A vertical line has Deltax=0\\Delta x=0, so its slope is undefined.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

A vertical line has Deltax=0\\Delta x=0, so its slope is undefined.

9. QuestionMultiple choice

Which rate is greater?

Please select an answer first.

Correct answer: A

The correct answer is frac34\\frac{3}{4}.

  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: frac34=0.75\\frac{3}{4}=0.75, which is greater than 0.6, frac23approx0.667\\frac{2}{3}\\approx0.667, and 0.5.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

frac34=0.75\\frac{3}{4}=0.75, which is greater than 0.6, frac23approx0.667\\frac{2}{3}\\approx0.667, and 0.5.

10. QuestionMultiple choice

A line changes from (2,5)(2,5) to (6,13)(6,13). What does its slope measure?

Please select an answer first.

Correct answer: B

The correct answer is The change in y for each one-unit change in x.

  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=frac13−56−2=2m=\\frac{13-5}{6-2}=2, meaning y increases by 2 for every 1-unit increase in x.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

m=frac13−56−2=2m=\\frac{13-5}{6-2}=2, meaning y increases by 2 for every 1-unit increase in x.

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