https://file.aiquickdraw.com/mathbot/file/1728348458280m4l1izxh.jpg

The problem asks to determine the slope of a given line (the blue line in the image) and to find the slope of a line perpendicular to it.

### Step 1: Determine the Slope of the Given Line
To find the slope of the given line, we can use the slope formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
From the graph, we can identify two points on the line. For example, the points \((-9, 9)\) and \((0, -2)\) appear to lie on the line.

\[
\text{slope} = \frac{-2 - 9}{0 - (-9)} = \frac{-11}{9}
\]
So, the slope of the given line is \(-\frac{11}{9}\).

### Step 2: Determine the Perpendicular Slope
The slope of a line perpendicular to another is the negative reciprocal of the original slope. Given that the original slope is \(-\frac{11}{9}\), the perpendicular slope will be:
\[
\text{perpendicular slope} = \frac{9}{11}
\]

### Final Answer:
- **Original Slope**: \(-\frac{11}{9}\)
- **Perpendicular Slope**: \(\frac{9}{11}\)

Would you like more details or have any questions about these steps?

Here are 5 related questions to expand on this:
1. How do we graph a line if we know its slope and a point on it?
2. What happens to the slope when lines are parallel?
3. How do you find the equation of a line if you're given the slope and a point?
4. How can we verify if two lines are perpendicular from their slopes?
5. What are some real-life applications of perpendicular lines?

**Tip**: When dealing with slopes, always remember that the perpendicular slope is the negative reciprocal of the original slope!

Graph a line that is perpendicular to the given line. Determine the slope of the given line and the one you graphed in simplest form.

Learn how to graph a line perpendicular to a given line and calculate the slope of both lines. The problem focuses on slope calculations and perpendicular relationships in coordinate geometry. Suitable for students in Grades 9-11.

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