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.

4. 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 y=3x+2y=3x+2?

Please select an answer first.

Correct answer: A

The correct answer is 33.

  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=mx+by=mx+b, the coefficient of x is the slope, 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.

In y=mx+by=mx+b, the coefficient of x is the slope, so m=3m=3.

2. QuestionMultiple choice

What is the slope of y=−4x+1y=-4x+1?

Please select an answer first.

Correct answer: B

The correct answer is −4-4.

  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: The coefficient of x is -4, so the line decreases 4 units in y for each 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.

The coefficient of x is -4, so the line decreases 4 units in y for each 1-unit increase in x.

3. QuestionMultiple choice

What is the slope of y=0.25x−7y=0.25x-7?

Please select an answer first.

Correct answer: C

The correct answer is 0.250.25.

  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 coefficient of x is 0.250.25, which is the slope.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

The coefficient of x is 0.250.25, which is the slope.

4. QuestionMultiple choice

What is the slope of the horizontal line y=5y=5?

Please select an answer first.

Correct answer: D

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 constant y-value, so its vertical change and slope are 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 constant y-value, so its vertical change and slope are 0.

5. QuestionMultiple choice

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

Please select an answer first.

Correct answer: A

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 no change in x between distinct points, so the denominator in the slope formula 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 vertical line has no change in x between distinct points, so the denominator in the slope formula is 0.

6. QuestionMultiple choice

What do the lines y=2x+1y=2x+1 and y=2x−5y=2x-5 have in common?

Please select an answer first.

Correct answer: B

The correct answer is They have the same slope and are parallel..

  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: Both equations have slope 2 but different y-intercepts, so they are distinct parallel lines.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Both equations have slope 2 but different y-intercepts, so they are distinct parallel lines.

7. QuestionMultiple choice

What is the equation of the line with slope −2-2 and y-intercept 33?

Please select an answer first.

Correct answer: C

The correct answer is y=−2x+3y=-2x+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: Substitute m=−2m=-2 and b=3b=3 into y=mx+by=mx+b.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

Substitute m=−2m=-2 and b=3b=3 into y=mx+by=mx+b.

8. QuestionMultiple choice

What is y when y=frac12x−4y=\\frac{1}{2}x-4 and x=8x=8?

Please select an answer first.

Correct answer: D

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: y=frac12(8)−4=4−4=0y=\\frac{1}{2}(8)-4=4-4=0.
  3. Interpret the result: State what the slope means in context and check that the units are output units per input unit.

y=frac12(8)−4=4−4=0y=\\frac{1}{2}(8)-4=4-4=0.

9. QuestionMultiple choice

A line changes from y=10 to y=-2 while x changes from 1 to 5. What is the slope?

Please select an answer first.

Correct answer: A

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: m=frac−2−105−1=frac−124=−3m=\\frac{-2-10}{5-1}=\\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=frac−2−105−1=frac−124=−3m=\\frac{-2-10}{5-1}=\\frac{-12}{4}=-3.

10. QuestionMultiple choice

Which form identifies the slope and y-intercept directly?

Please select an answer first.

Correct answer: B

The correct answer is y=mx+by=mx+b.

  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, mm is the slope and bb is the y-intercept.
  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, mm is the slope and bb is the y-intercept.