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!