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Let's analyze the problem step by step:

We have two linear functions, Function A and Function B:

- Function A is represented by a table of values:

| x  | y   |
|----|-----|
| -6 | -10 |
| -3 | -5  |
| 9  | 15  |

- Function B is given by the equation \( y = \frac{4}{3}x - 3 \).

The question asks about the y-values of both functions when \( x = 6 \).

### 1. **Determine the equation for Function A:**
We need to find the equation for Function A. Since it is a linear function, we can calculate its slope (\( m \)) using two points from the table. Let's use the points \( (-6, -10) \) and \( (-3, -5) \).

The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-10)}{-3 - (-6)} = \frac{-5 + 10}{-3 + 6} = \frac{5}{3}
\]

So, the slope of Function A is \( \frac{5}{3} \).

Now, let's use the point-slope form of the line equation to find the full equation. Using the point \( (-3, -5) \):
\[
y - y_1 = m(x - x_1)
\]
\[
y - (-5) = \frac{5}{3}(x - (-3))
\]
\[
y + 5 = \frac{5}{3}(x + 3)
\]
Expanding:
\[
y + 5 = \frac{5}{3}x + 5
\]
\[
y = \frac{5}{3}x
\]
Thus, the equation of Function A is \( y = \frac{5}{3}x \).

### 2. **Find the y-value of Function A when \( x = 6 \):**
Using the equation \( y = \frac{5}{3}x \):
\[
y = \frac{5}{3} \times 6 = 10
\]
So, when \( x = 6 \), the y-value of Function A is 10.

### 3. **Find the y-value of Function B when \( x = 6 \):**
Using the equation \( y = \frac{4}{3}x - 3 \):
\[
y = \frac{4}{3} \times 6 - 3 = 8 - 3 = 5
\]
So, when \( x = 6 \), the y-value of Function B is 5.

### 4. **Conclusion:**
When \( x = 6 \), the y-value of Function A is 10, and the y-value of Function B is 5. Therefore, the correct statement is:

**"The y-value of Function A when x = 6 is greater than the y-value of Function B when x = 6."**

Let me know if you'd like further details or have any questions! Here are some related questions to expand on:

1. What is the significance of slope in a linear equation?
2. How can you determine the y-intercept from a table of values?
3. What does it mean for two linear functions to have the same slope?
4. How do you graph a linear function from its equation?
5. What is the relationship between the slope and the rate of change?

**Tip:** When finding the equation of a line from a table, always use the slope formula and a known point to derive the equation.

Which statement is true: The y-value of Function A when x = 6 is greater than the y-value of Function B when x = 6, or The y-value of Function A when x = 6 is less than the y-value of Function B when x = 6?

Compare the y-values of two linear functions, A and B, when x = 6. Learn how to determine the slope and the equation of a line from a table and calculate values for both functions.

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