Students solve slope problems in a maze format to find the correct path from start to finish.

Problem: Finding the Slope Maze

The task is to solve a maze by finding the slope of various lines or equations and using the answers to navigate through the maze. The goal is to start at the "START HERE!" square and move to the "FINISHED!" square.

#### Step-by-Step Solution:

1. Start Here!
- Coordinates: (2, 5) and (0, -1)
- Formula for slope: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
- Substituting the points:
\[
m = \frac{-1 - 5}{0 - 2} = \frac{-6}{-2} = 3
\]
- Move to the square with \( m = 3 \).

2. Next Square: \( m = 3 \)
- Equation: \( 5x - 15y = 10 \)
- Rewrite in slope-intercept form \( y = mx + b \):
\[
5x - 15y = 10 \implies -15y = -5x + 10 \implies y = \frac{1}{3}x - \frac{2}{3}
\]
- Slope \( m = \frac{1}{3} \)
- Move to the square with \( m = \frac{1}{3} \).

3. Next Square: \( m = \frac{1}{3} \)
- Graph: The graph shows a line with a positive slope.
- By visually inspecting the graph, the slope appears to be \( m = -\frac{2}{5} \).
- Move to the square with \( m = -\frac{2}{5} \).

4. Next Square: \( m = -\frac{2}{5} \)
- Table:
\[
\begin{array}{c|c}
x & y \\
\hline
3 & 24 \\
6 & 18 \\
9 & 12 \\
12 & 6 \\
\end{array}
\]
- Calculate the slope using two points, e.g., (3, 24) and (6, 18):
\[
m = \frac{18 - 24}{6 - 3} = \frac{-6}{3} = -2
\]
- Move to the square with \( m = -2 \).

5. Next Square: \( m = -2 \)
- Equation: \( 2x - 10y = -50 \)
- Rewrite in slope-intercept form:
\[
2x - 10y = -50 \implies -10y = -2x - 50 \implies y = \frac{1}{5}x + 5
\]
- Slope \( m = \frac{1}{5} \)
- Move to the square with \( m = \frac{1}{5} \).

6. Next Square: \( m = \frac{1}{5} \)
- Table:
\[
\begin{array}{c|c}
x & y \\
\hline
1 & 4 \\
2 & 3 \\
3 & 2 \\
4 & 1 \\
\end{array}
\]
- Calculate the slope using two points, e.g., (1, 4) and (2, 3):
\[
m = \frac{3 - 4}{2 - 1} = \frac{-1}{1} = -1
\]
- Move to the square with \( m = -1 \).

7. Next Square: \( m = -1 \)
- Points: (4, -8) and (4, -3)
- Notice that the x-coordinates are the same, indicating a vertical line.
- Slope of a vertical line is undefined.
- Move to the square with \( m = \text{undefined} \).

8. Next Square: \( m = \text{undefined} \)
- Graph: The graph shows a vertical line.
- Vertical lines have an undefined slope.
- Move to the square with \( m = 1 \).

9. Next Square: \( m = 1 \)
- Graph: The graph shows a line with a positive slope.
- By visually inspecting the graph, the slope appears to be \( m = 2 \).
- Move to the square with \( m = 2 \).

10. Next Square: \( m = 2 \)
- Table:
\[
\begin{array}{c|c}
x & y \\
\hline
2 & 1 \\
4 & 2 \\
6 & 3 \\
8 & 4 \\
\end{array}
\]
- Calculate the slope using two points, e.g., (2, 1) and (4, 2):
\[
m = \frac{2 - 1}{4 - 2} = \frac{1}{2}
\]
- Move to the square with \( m = \frac{1}{2} \).

11. Next Square: \( m = \frac{1}{2} \)
- Points: (5, 3) and (10, 5)
- Calculate the slope:
\[
m = \frac{5 - 3}{10 - 5} = \frac{2}{5}
\]
- Move to the square with \( m = \frac{2}{5} \).

12. Next Square: \( m = \frac{2}{5} \)
- Graph: The graph shows a horizontal line.
- Horizontal lines have a slope of 0.
- Move to the square with \( m = 0 \).

13. Next Square: \( m = 0 \)
- Final destination: "FINISHED!"

Final Answer:

\[
\boxed{\text{FINISHED!}}
\]