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

Function A

Function A is given as a table of values:

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.