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To address the task, let's analyze both functions and compare their properties:

### Function A
Function A is given as a table of values:

| x  | y  |
|----|----|
| -9 | -6 |
| -6 | -5 |
|  9 |  0 |

To find the slope of Function A, we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-9, -6)\) and \( (9, 0)\):
\[
m = \frac{0 - (-6)}{9 - (-9)} = \frac{6}{18} = \frac{1}{3}
\]

### Function B
Function B is represented graphically. We need to pick two points from the line to calculate its slope. By inspection, using points \((0, 0)\) and \((10, 10)\):
\[
m = \frac{10 - 0}{10 - 0} = 1
\]

### Comparing the Statements
- **The slope of Function A is less than the slope of Function B.**
  - True. The slope of A is \(\frac{1}{3}\) and B is \(1\).

- **The slope of Function A is equal to the slope of Function B.**
  - False. As determined above.

- **The y-value of Function A when \(x = 6\) is equal to the y-value of Function B when \(x = 6\).**
  - To find the y-value for Function A when \(x = 6\), use the slope-intercept form, noting the point \((-6, -5)\) for determining the intercept:
    \[
    y = \frac{1}{3}x + b
    \]
    \[
    -5 = \frac{1}{3}(-6) + b \implies -5 = -2 + b \implies b = -3
    \]
    \[
    y = \frac{1}{3}x - 3
    \]
    \[
    y(6) = \frac{1}{3}(6) - 3 = 2 - 3 = -1
    \]
    For Function B, since the slope is \(1\) and the y-intercept is \(0\):
    \[
    y(6) = 1(6) = 6
    \]
    - False. Function A yields \(-1\) and Function B yields \(6\) at \(x = 6\).

- **The y-value of Function A when \(x = 6\) is greater than the y-value of Function B when \(x = 6\).**
  - False. As shown, \(-1\) is not greater than \(6\).

Do you need more detailed calculations or have any other questions on this? Here are some related queries:

1. How can we determine the y-intercept of Function B from its graph?
2. What happens to the y-values of Function A as \(x\) increases further?
3. Can we write the equation of Function B using point-slope form?
4. How would Function A's graph look if plotted?
5. Are there any x-values where Functions A and B intersect?

**Tip:** When analyzing a linear function from a graph or table, always verify the slope and intercept by checking calculations with multiple points to ensure accuracy.

The problem asks to analyze two linear functions, A and B, to determine their slopes and compare specific y-values at x = 6.

Learn how to analyze and compare the slopes of two linear functions A and B, and determine their y-values at x = 6. This problem uses slope calculation and graph interpretation for students in Grades 8-10.

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