Slope Sleuths Activity Worksheet
Early Finisher Activity Grade 8 • Linear Basics
Slope Sleuths: Line Explorer
Finished your classwork early? Discover the secrets of \(y = mx + b\) with fun visual puzzles!
Sleuth Name:
Date: Period:
\(y = \mathbf{m}x + \mathbf{b}\)
• \(\mathbf{m}\) = Slope: \(\frac{\text{Rise (Up/Down)}}{\text{Run (Right)}}\) • Positive = Uphill \(\nearrow\), Negative = Downhill \(\searrow\)
• \(\mathbf{b}\) = \(y\)-Intercept: Starting spot on vertical \(y\)-axis: Point \((0, b)\)
1 Clue Station 1: The Equation Decoder
Spot \(m\) and \(b\), and circle the line direction!
\(y = 3x + 2\) Line A
Slope \(m\) = _____
\(y\)-intercept \(b\) = _____
Start: \((0, \text{____})\)
Circle: Uphill / Downhill
\(y = -2x + 5\) Line B
Slope \(m\) = _____
\(y\)-intercept \(b\) = _____
Start: \((0, \text{____})\)
Circle: Uphill / Downhill
\(y = \frac{1}{2}x - 4\) Line C
Slope \(m\) = _____
\(y\)-intercept \(b\) = _____
Start: \((0, \text{____})\)
Circle: Uphill / Downhill
\(y = -4x\) Line D (\(b = ?\))
Slope \(m\) = _____
\(y\)-intercept \(b\) = _____
Start: \((0, \text{____})\)
Circle: Uphill / Downhill
2 Clue Station 2: Real-Life Stories • What Do the Numbers Mean?
Connect the math to everyday life!
Electric Scooter: \(y = 2x + 3\)
An app charges $3 to unlock plus $2 per mile \(x\).
• What does the $3 represent? __________________________
• What does the $2 represent? __________________________
• Cost for 4 miles: \(y = 2(4) + 3 = \mathbf{\$}\)______
Melting Snowman: \(y = -3x + 30\)
Snowman is 30 inches tall and melts 3 inches per hour \(x\).
• Why is slope negative (\(-3\))? ________________________
• What does 30 represent? __________________________
• Height after 4 hours: \(y = -3(4) + 30 =\) ______ inches
3 Clue Station 3: Mystery Table Detective
Find \(b\) when \(x = 0\) and discover the pattern \(m\)!
| \(x\) |
\(y\) |
| 0 |
4 |
| 1 |
7 |
| 2 |
10 |
| 3 |
13 |
1. When \(x = 0\), what is \(y\)? \(b =\) ______
2. How much does \(y\) grow each step? \(m =\) ______
Equation: \(y =\) ____________
| \(x\) |
\(y\) |
| 0 |
10 |
| 1 |
8 |
| 2 |
6 |
| 3 |
4 |
1. When \(x = 0\), what is \(y\)? \(b =\) ______
2. Does \(y\) go up or down? By how much? \(m =\) ______
Equation: \(y =\) ____________
Slope Sleuths Activity • Beginner Early Finisher Packet • Page 1 of 2 Turn over for 3-Step Graphing & Celestial Target Practice!
Part 2 Target Practice & Graphing
Clue Station 4 & 5: Graphing & Celestial Target Lock
Hands-On Practice
4 The 3-Step Graphing Strategy
Step 1: Plot \(b\) on \(y\)-axis → Step 2: Count \(\frac{\text{rise}}{\text{run}}\) → Step 3: Draw line
\(y = 2x - 3\) Slope \(m = \frac{2}{1}\), \(b = -3\)
x y 0 4 -4 4 -4
• 1st Dot: Start at \((0, \mathbf{-3})\).
• 2nd Dot: Go UP 2, RIGHT 1 to \((1, \mathbf{-1})\).
• 3rd Dot: Go UP 2, RIGHT 1 to \((2, \mathbf{1})\). Connect!
\(y = -\frac{1}{2}x + 2\) Slope \(m = \frac{-1}{2}\), \(b = 2\)
x y 0 4 -4 4 -4
• 1st Dot: Start at \((0, \mathbf{2})\).
• 2nd Dot: Go DOWN 1, RIGHT 2 to \((2, \mathbf{1})\).
• 3rd Dot: Go DOWN 1, RIGHT 2 to \((4, \mathbf{0})\). Connect!
5 Clue Station 5: Celestial Target Lock Game
Which line hits which target?
Star (2, 3) Moon (-3, 1) Planet (3, -2)
Laser 1: \(y = x + 1\)
Starts at \((0, 1)\), up 1, right 1. When \(x = 2\): \(y = (2) + 1 = \) ______
Which target does Laser 1 hit? _______________
Laser 2: \(y = -2x + 4\)
Starts at \((0, 4)\), down 2, right 1. When \(x = 3\): \(y = -2(3) + 4 = \) ______
Which target does Laser 2 hit? _______________
Creative Lab
Clue Station 6: Build Your Own Mystery Line Riddle
Design Challenge
Create a mystery line for a classmate to solve. Choose your slope and starting point:
• Choose slope: m = _____ • Choose start: b = _____
Your Equation: \(y =\) ____________
Write a 1-sentence real-world clue for your line:
Slope Sleuths Activity • Grade 8 Linear Basics • Early Finisher Extension Great job! Ask a classmate to solve your Mystery Line Riddle!
Slope Sleuths Activity Answer Key
Teacher Key Beginner Early Finisher
Slope Sleuths Activity Answer Key
Complete solutions, explanation keys, and teaching tips for Stations 1–3
Grade 8 Mathematics
Introductory Linear Functions
1 Station 1: Equation Decoder Solutions
4 Items • 8 Pts
Line A: \(y = 3x + 2\) Positive Slope
• Slope \(m = \mathbf{3}\) (or \(\frac{3}{1}\)) • \(y\)-intercept \(b = \mathbf{2}\)
• Starting Point: \(\mathbf{(0, 2)}\) • Direction: Uphill \(\nearrow\)
Line B: \(y = -2x + 5\) Negative Slope
• Slope \(m = \mathbf{-2}\) (or \(\frac{-2}{1}\)) • \(y\)-intercept \(b = \mathbf{5}\)
• Starting Point: \(\mathbf{(0, 5)}\) • Direction: Downhill \(\searrow\)
Line C: \(y = \frac{1}{2}x - 4\) Fractional Slope
• Slope \(m = \mathbf{\frac{1}{2}}\) (Rise 1, Run 2) • \(y\)-intercept \(b = \mathbf{-4}\)
• Starting Point: \(\mathbf{(0, -4)}\) • Direction: Uphill \(\nearrow\)
Line D: \(y = -4x\) Origin Intercept
• Slope \(m = \mathbf{-4}\) • \(y\)-intercept \(b = \mathbf{0}\) (origin!)
• Starting Point: \(\mathbf{(0, 0)}\) • Direction: Downhill \(\searrow\)
2 Station 2: Real-Life Stories Solutions
6 Pts
Scooter Rental (\(y = 2x + 3\))
• $3 meaning: The initial unlock fee (starting cost at 0 miles).
• $2 meaning: Rate of change (the cost per each additional mile).
• 4-mile calculation: \(y = 2(4) + 3 = 8 + 3 = \mathbf{\$11}\).
Melting Snowman (\(y = -3x + 30\))
• Why slope is negative: The snowman loses height / shrinks as time passes.
• 30 meaning: Initial height (starting height at 0 hours).
• 4-hour calculation: \(y = -3(4) + 30 = -12 + 30 = \mathbf{18\text{ inches}}\).
3 Station 3: Mystery Table Detective Solutions
6 Pts
Table A Analysis
1. At \(x = 0\), \(y = 4\), so \(b = \mathbf{4}\).
2. \(y\) increases by \(+3\) each step, so \(m = \mathbf{3}\).
Equation: \(y = 3x + 4\)
Table B Analysis
1. At \(x = 0\), \(y = 10\), so \(b = \mathbf{10}\).
2. \(y\) decreases by \(-2\) each step, so \(m = \mathbf{-2}\).
Equation: \(y = -2x + 10\)
Teacher Facilitation Tip for Beginners:
Remind students that the \(y\)-intercept is always on the vertical flagpole (\(y\)-axis), not the horizontal ground (\(x\)-axis). If an early finisher finishes quickly, invite them to act as a "Sleuth Coach" for a peer!
Slope Sleuths Activity Key • Page 1 of 2 Turn over for Graph Keys & Celestial Target Answers
Station 4–6: Graphing & Target Key
Visual plot verification, celestial target solutions, and creative riddle rubric
Page 2 of 2
4 Station 4: Step-by-Step Graphing Keys
6 Pts
Graph A Key: \(y = 2x - 3\) Passes (0, -3)
Plotted checkpoints: \((0, -3), (1, -1), (2, 1), (3, 3)\)
Graph B Key: \(y = -\frac{1}{2}x + 2\) Passes (0, 2)
Plotted checkpoints: \((0, 2), (2, 1), (4, 0), (-2, 3)\)
5 Station 5: Celestial Target Lock Solutions
4 Pts
Laser Beam 1: \(y = x + 1\)
Testing \(x = 2\): \(y = 2 + 1 = \mathbf{3}\). This matches coordinate \((2, 3)\).
• Laser 1 hits the: STAR \(\bigstar\) at \((2, 3)\)!
Laser Beam 2: \(y = -2x + 4\)
Testing \(x = 3\): \(y = -2(3) + 4 = -6 + 4 = \mathbf{-2}\). This matches coordinate \((3, -2)\).
• Laser 2 hits the: PLANET \(\odot\) at \((3, -2)\)!
Rubric
Station 6: Riddle Creation Rubric
Peer Challenge
Sample Student Response:
• Chosen Slope: \(m = 4\), Chosen Intercept: \(b = 10\).
• Equation: \(y = 4x + 10\).
• Riddle Clue: "A plant starts at 10 inches tall and grows 4 inches each week."
Grading criteria: Student successfully links their slope \(m\) to a rate (per unit) and their \(y\)-intercept \(b\) to a starting amount.
Slope Sleuths Activity Key • Grade 8 Linear Basics Total Points: 24 Points • Encouraging and Accessible for All Learners
