Let's solve the problem by analyzing the slopes of both functions, $A$ and $B$.

Function A:

From the graph of Function A, we can calculate the slope by identifying two points on the line. The slope is calculated as: $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Looking at the graph:

• One point is $(0, 0)$ (the origin).
• Another point is $(2, 4)$.

So, the slope of Function A is: $\text{slope of A} = \frac{4 - 0}{2 - 0} = \frac{4}{2} = 2$

Function B:

To calculate the slope of Function B, we will use the two points from the table provided:

• $(-4, -14)$
• $(-2, -6)$

The slope formula for Function B is: $\text{slope of B} = \frac{-6 - (-14)}{-2 - (-4)} = \frac{-6 + 14}{-2 + 4} = \frac{8}{2} = 4$

Comparison:

• The slope of Function A is $2$.
• The slope of Function B is $4$.

Thus, the correct statement is: The slope of Function A is less than the slope of Function B.

Would you like any additional details or have any questions?

Related Questions:

1. How do you calculate the slope when given two points?
2. What does the slope represent in a linear function?
3. How do you determine if two lines are parallel based on their slopes?
4. Can two lines with the same slope have different y-intercepts?
5. How does changing the slope affect the steepness of a line?

Tip:

When comparing slopes, larger absolute values indicate steeper lines.