Testinar Grade 8 math

Slope as Rate of Change

Learn to reason about and solve Grade 8 problems involving Slope as Rate of Change.

CH03-02 Equations, Inequalities, and Systems
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. What is the slope of the line shown? \par

    Slope as Rate of Change visual for G8-C03-T02-Q002
    1. \(2\)
    2. \(\frac{1}{3}\)
    3. \(3\)
    4. \(\frac{3}{2}\)

  2. A table shows the relationship between hours worked and pay earned. \par What is the rate of change (slope) of pay with respect to hours worked?

    Slope as Rate of Change visual for G8-C03-T02-Q003
    1. \($8\) per hour
    2. \($12\) per hour
    3. \($10\) per hour
    4. \($9\) per hour

  3. A car travels at a constant speed. The graph shows its distance from the start over time. \par What is the slope (rate of change) of the car's distance?

    Slope as Rate of Change visual for G8-C03-T02-Q004
    1. \(1\) mile per hour
    2. \(\frac{4}{3}\) miles per hour
    3. \(\frac{3}{4}\) miles per hour
    4. \(4\) miles per hour

  4. The graph shows elevation change during a hike. \par What is the slope of the line?

    Slope as Rate of Change visual for G8-C03-T02-Q006
    1. \(\frac{3}{4}\)
    2. \(\frac{2}{3}\)
    3. \(\frac{3}{2}\)
    4. \(2\)

  5. A student earns $15 per hour. Which table represents this relationship? \par What is the slope?

    Slope as Rate of Change visual for G8-C03-T02-Q008
    1. \(15\)
    2. \(\frac{1}{15}\)
    3. \(30\)
    4. \(\frac{15}{30}\)

  6. A table shows values for \(x\) and \(y\). What is the rate of change? \par

    Slope as Rate of Change visual for G8-C03-T02-Q014
    1. \(2\)
    2. \(\frac{1}{2}\)
    3. \(4\)
    4. \(-2\)

  7. Which graph represents a positive slope? \par

    Slope as Rate of Change visual for G8-C03-T02-Q020
    1. Red line (left)
    2. Blue line (right)
    3. Both have positive slope
    4. Neither has positive slope

  8. A graph shows depth of water versus time as a pool is filled. \par What is the filling rate (slope)?

    Slope as Rate of Change visual for G8-C03-T02-Q022
    1. \(\frac{4}{5}\) inches per minute
    2. \(\frac{5}{4}\) inches per minute
    3. \(4\) inches per minute
    4. \(5\) inches per minute
Teacher and parent reference

Answer key and explanations

  1. C. \(3\)

    The line passes through \((0,0)\) and \((1,3)\). Rise is \(3\) for every \(1\) unit right. The slope is \(\frac{\text{rise}}{\text{run}}=\frac{3}{1}=3\).

  2. D. \($9\) per hour

    Choose two points from the table: \((2, 18)\) and \((4, 36)\). Slope \(= \frac{36-18}{4-2}=\frac{18}{2}=9\) dollars per hour.

  3. C. \(\frac{3}{4}\) miles per hour

    The rise is \(3\) miles and the run is \(4\) hours. Slope \(= \frac{3}{4}\) miles per hour. This is the constant speed.

  4. C. \(\frac{3}{2}\)

    From \((1,1)\) to \((3,4)\): slope \(=\frac{4-1}{3-1}=\frac{3}{2}\).

  5. A. \(15\)

    Using points \((1,15)\) and \((2,30)\): slope \(=\frac{30-15}{2-1}=\frac{15}{1}=15\) dollars per hour.

  6. A. \(2\)

    Using any two points, e.g., \((0,-2)\) and \((2,2)\): slope \(=\frac{2-(-2)}{2-0}=\frac{4}{2}=2\).

  7. A. Red line (left)

    The red line goes up as \(x\) increases (positive slope). The blue line goes down as \(x\) increases (negative slope).

  8. A. \(\frac{4}{5}\) inches per minute

    From \((0,0)\) to \((5,4)\): slope \(=\frac{4-0}{5-0}=\frac{4}{5}\) inches per minute.

Free Testinar sample Reviewed November 6, 2026 testinar.com
Page UP