Geometry Worksheets - Free Printable

Since I can't view or access images directly, I can't see the specific houses or graphs in your uploaded image. However, based on the description of the task — "Find the slope of each roof. (One slope should be positive)" — and the typical format of such problems, I can guide you through solving this type of problem step-by-step.

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🔍 Understanding the Task

You're given a series of house drawings with triangular roofs plotted on a grid. The goal is to find the slope of the roof, which is the slope of the line forming the roof's edge (usually one side of the triangle).

Slope is calculated using the formula:

$$
\text{Slope} = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
$$

You'll need to pick two points on the roof’s edge (the slanted line), then compute the slope.

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🧩 Step-by-Step Instructions

1. Identify the two endpoints of the roof's edge (top peak and bottom corner).
2. Use the grid to determine the coordinates of these points.
3. Apply the slope formula.
4. Simplify the fraction if needed.
5. Note: One roof will have a positive slope, others may be negative or zero.

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✔ Example (Hypothetical)

Suppose for one house:
- The top of the roof is at (2, 6)
- The bottom-left corner is at (0, 2)

Then:
$$
\text{Slope} = \frac{6 - 2}{2 - 0} = \frac{4}{2} = 2
$$

So, the slope is 2 (positive).

Now suppose another roof goes from (4, 6) to (6, 2):
$$
\text{Slope} = \frac{2 - 6}{6 - 4} = \frac{-4}{2} = -2
$$

So, the slope is -2 (negative).

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⚠️ Important Notes

- Positive slope: Roof slopes upward from left to right.
- Negative slope: Roof slopes downward from left to right.
- Since it says “one slope should be positive,” likely only one roof has an upward slope when viewed from left to right.

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💡 Tips

- Always use the same two points on the same side of the roof.
- If the roof is symmetric, both sides may have equal but opposite slopes.
- Double-check your rise and run — count up/down and left/right carefully.

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📝 Final Answer Format

For each house, write:
> Slope = [value]

Example:
> Slope = 2
> Slope = -1
> Slope = 0
> etc.

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If you can describe the positions of the roofs (e.g., "House A has a peak at (3,5) and base corners at (1,2) and (5,2)"), I can help calculate the exact slopes for each one.

Let me know!