Finding Slope Digital Maze - Lindsay Bowden - Free Printable

Let’s solve the Finding Slope Maze step by step.

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🎯 Goal:

Start at “START HERE!” and follow the correct slope (m) from each box to the next, until you reach “FINISHED!”

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## 🔢 Step 1: Start Here! — Points (2,5) and (0,-1)

Use the slope formula:
> m = (y₂ - y₁) / (x₂ - x₁)

Let’s plug in:
- (x₁, y₁) = (2, 5)
- (x₂, y₂) = (0, -1)

→ m = (-1 - 5) / (0 - 2) = (-6) / (-2) = 3

✔ So, we move along the path labeled m = 3

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## ➡️ Step 2: From m=3 → Next Box: 5x - 15y = 10

We need to find the slope of this line. Let’s convert it to slope-intercept form (y = mx + b).

Start with:
> 5x - 15y = 10

Subtract 5x from both sides:
> -15y = -5x + 10

Divide everything by -15:
> y = (5/15)x - 10/15
> y = (1/3)x - 2/3

✔ So, m = 1/3

→ Move along the path labeled m = 1/3

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## ➡️ Step 3: From m=1/3 → Next Box: Graph with line going down to the right

This is a graph. We can pick two points on the line.

Looking at the graph:
- It passes through (0, 0) and maybe (4, -2)? Or let's count grid squares.

From (0,0), if we go right 2 units, down 1 unit → slope = rise/run = -1/2

✔ So, m = -1/2

→ Move along the path labeled m = -1/2

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## ➡️ Step 4: From m=-1/2 → Next Box: Table with x and y values

Table:

| x | y |
|---|---|
| 3 | 24 |
| 6 | 18 |
| 9 | 12 |
|12 | 6 |

Pick any two points, say (3,24) and (6,18)

→ m = (18 - 24)/(6 - 3) = (-6)/3 = -2

✔ So, m = -2

→ Move along the path labeled m = -2

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## ➡️ Step 5: From m=-2 → Next Box: Equation 2x - 10y = -50

Convert to slope-intercept form:

> 2x - 10y = -50

Subtract 2x:
> -10y = -2x - 50

Divide by -10:
> y = (2/10)x + 5
> y = (1/5)x + 5

✔ So, m = 1/5

→ Move along the path labeled m = 1/5

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## ➡️ Step 6: From m=1/5 → Next Box: Table

Table:

| x | y |
|---|---|
| 1 | 4 |
| 2 | 3 |
| 3 | 2 |
| 4 | 1 |

Pick (1,4) and (2,3):

→ m = (3 - 4)/(2 - 1) = (-1)/1 = -1

✔ So, m = -1

→ Move along the path labeled m = -1

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## ➡️ Step 7: From m=-1 → Next Box: Points (4, -8) and (4, -3)

Wait — same x-value? That means vertical line!

Slope = (y₂ - y₁)/(x₂ - x₁) = (-3 - (-8))/(4 - 4) = 5/0 → undefined

✔ So, m = undefined

→ Move along the path labeled m = undefined

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## ➡️ Step 8: From m=undefined → Next Box: Graph with diagonal line through origin

This graph shows a line going up to the right. Pick two points: (0,0) and (3,3)

→ m = (3 - 0)/(3 - 0) = 3/3 = 1

✔ So, m = 1

→ Move along the path labeled m = 1

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## ➡️ Step 9: From m=1 → Next Box: Points (5,3) and (10,5)

→ m = (5 - 3)/(10 - 5) = 2/5

✔ So, m = 2/5

→ Move along the path labeled m = 2/5

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## ➡️ Step 10: From m=2/5 → Next Box: Horizontal line graph

Horizontal line → slope = 0

✔ So, m = 0

→ Move along the path labeled m = 0

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## ✔ FINAL STEP: From m=0 → “FINISHED!”

You’ve reached the end!

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## 🧭 Path Summary (for reference):

1. START → (2,5) & (0,-1) → m=3
2. → 5x - 15y = 10 → m=1/3
3. → Graph (downward line) → m=-1/2
4. → Table (x=3,y=24 etc.) → m=-2
5. → 2x - 10y = -50 → m=1/5
6. → Table (x=1,y=4 etc.) → m=-1
7. → (4,-8) & (4,-3) → m=undefined
8. → Diagonal graph → m=1
9. → (5,3) & (10,5) → m=2/5
10. → Horizontal line → m=0
11. → FINISHED!

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✔ You’ve successfully navigated the maze!

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📌 Note: If you were to draw the path, it would trace:
Start → 3 → 1/3 → -1/2 → -2 → 1/5 → -1 → undefined → 1 → 2/5 → 0 → Finished!

Great job solving the maze! 🎉