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To find the slope of the line that is perpendicular to the given line, we first need to determine the slope of the line shown on the graph.

### Step 1: Calculate the slope of the given line
The slope \( m \) of a line is given by the formula:

\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

From the graph, we can select two points on the line:
- Point 1: \( (-6, -6) \)
- Point 2: \( (0, 7) \)

Now, calculate the slope:

\[
m = \frac{7 - (-6)}{0 - (-6)} = \frac{7 + 6}{0 + 6} = \frac{13}{6}
\]

So, the slope of the given line is \( \frac{13}{6} \).

### Step 2: Determine the slope of the perpendicular line
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. If the slope of the given line is \( m \), then the slope of the perpendicular line is:

\[
m_{\perp} = -\frac{1}{m} = -\frac{1}{\frac{13}{6}} = -\frac{6}{13}
\]

However, the question asks for the slope of a line **perpendicular** to the line, and none of the provided options matches \(-\frac{6}{13}\). It seems there might be a mistake in either the interpretation of the graph or the options provided. If you'd like, we can review the graph further or reevaluate the options for more clarity.

Would you like further details, or should we analyze another aspect of the problem?

Here are 5 related questions:
1. What is the general relationship between the slopes of perpendicular lines?
2. How do you find the slope of a line if only two points are given?
3. What is the significance of the slope in determining the steepness of a line?
4. How do negative reciprocals work in slope calculations?
5. Can a vertical line have a perpendicular slope, and if so, what would it be?

**Tip:** When dealing with perpendicular lines, always remember that their slopes are negative reciprocals of each other.

What is the slope of the line that is perpendicular to the given line?

Learn how to find the slope of a line perpendicular to a given line using graph coordinates. This question covers geometry concepts like slopes, perpendicularity, and how to calculate the negative reciprocal for the perpendicular slope.

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