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:

• 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.