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We are asked to determine which proportion correctly represents the slope of the line containing points \( R \), \( S \), and \( T \).

### Step 1: Identify Coordinates
From the graph, we can determine the coordinates of the points \( R \), \( S \), and \( T \):
- \( R = (-11, 6) \)
- \( S = (-9, 2) \)
- \( T = (-6, -4) \)

### Step 2: Slope Formula
The slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We need to calculate the slope for the lines containing \( R \) and \( S \), as well as \( S \) and \( T \), to match it with one of the provided choices.

#### Slope between \( R (-11, 6) \) and \( S (-9, 2) \):
\[
m_{RS} = \frac{2 - 6}{-9 - (-11)} = \frac{-4}{2} = -2
\]

#### Slope between \( S (-9, 2) \) and \( T (-6, -4) \):
\[
m_{ST} = \frac{-4 - 2}{-6 - (-9)} = \frac{-6}{3} = -2
\]

The slopes are the same, confirming the line is straight, and the slope is \( -2 \).

### Step 3: Match with the Proportions
Looking at the given choices, we need to find a proportion that reflects the slope \( m = -2 \). Checking option **A**:

\[
\frac{6 - (-4)}{-11 - (-6)} = \frac{6 + 4}{-11 + 6} = \frac{10}{-5} = -2
\]

And:

\[
\frac{6 - 2}{-11 - (-9)} = \frac{4}{-2} = -2
\]

Both parts of option **A** give a slope of \( -2 \), so **A** is the correct choice.

### Final Answer: **A**

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Would you like more details, or do you have any questions?

Here are 5 related questions for further practice:
1. How do you calculate the slope between two points if both points have negative coordinates?
2. What does it mean if two segments have the same slope?
3. How can you verify if three points lie on the same straight line using slope?
4. How can you represent the slope between two points algebraically using only their coordinates?
5. How do you determine if two triangles are similar based on the slopes of their corresponding sides?

**Tip:** When calculating the slope, be careful with signs, especially when subtracting negative numbers!

Which proportion represents the slope of the line containing R, S, and T?

This problem helps students learn how to calculate the slope between three points, R, S, and T, using the slope formula. It involves using coordinates and analyzing proportions to match with given choices, and emphasizes understanding of lines and triangle similarity. Suitable for Grades 8-10.

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