Let's break this down step by step:

Function A:

Looking at the graph of Function A, we can determine the slope. The slope ($m$) of a line is calculated as the change in $y$ divided by the change in $x$, or:

$m = \frac{\Delta y}{\Delta x}$

From the graph, let's take two clear points on the line. The line crosses the points $(-4, 0)$ and $(0, 2)$.

So the change in $y$ is: $\Delta y = 2 - 0 = 2$ And the change in $x$ is: $\Delta x = 0 - (-4) = 4$ Thus, the slope of Function A is: $m_A = \frac{2}{4} = \frac{1}{2}$

Function B:

For Function B, we can calculate the slope using the given table. To find the slope, we use the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let's take two points from the table, $(-4, -24)$ and $(-1, -9)$:

$m_B = \frac{-9 - (-24)}{-1 - (-4)} = \frac{-9 + 24}{-1 + 4} = \frac{15}{3} = 5$

Comparing Slopes:

• Slope of Function A: $\frac{1}{2}$
• Slope of Function B: $5$

Clearly, the slope of Function A is less than the slope of Function B.

Conclusion:

The correct statement is:

• "The slope of Function A is less than the slope of Function B."

Would you like further details or have any other questions?

Related Questions:

1. How can we graph linear functions if only the slope and one point are known?
2. What is the significance of the slope in real-world scenarios?
3. How do changes in the slope affect the steepness of a line?
4. Can we determine the y-intercept of a line from its equation?
5. How do we find the equation of a line given two points?

Tip: Remember that a positive slope means the line rises as $x$ increases, while a negative slope means it falls.