The problem shows two linear functions, A and B:

• Function A is represented by the graph.
• Function B is given by the equation $y = 5x - 1$.

We are tasked with comparing the slopes of these two functions.

1. Slope of Function A (from the graph):

To find the slope of Function A, we can use two points on the line from the graph. Let's choose:

• Point 1: $(0, -6)$ (the y-intercept)
• Point 2: $(4, 4)$

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the values from the two points: $m = \frac{4 - (-6)}{4 - 0} = \frac{4 + 6}{4} = \frac{10}{4} = 2.5$ So, the slope of Function A is $2.5$.

2. Slope of Function B (from the equation):

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. From the equation $y = 5x - 1$, we can see that the slope of Function B is $5$.

Comparison:

• The slope of Function A is $2.5$.
• The slope of Function B is $5$.

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

The correct answer is: The slope of Function A is less than the slope of Function B.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

1. How do we interpret the y-intercept of a linear function?
2. What is the significance of the slope in real-world contexts?
3. Can you explain how to convert a graph into an equation?
4. How would the graph of Function B look compared to Function A?
5. How do we determine if two lines are parallel based on their slopes?

Tip: For any linear equation, the number next to $x$ is always the slope.