To solve this problem, let's determine the slope of each function and compare them.

Function A (Graph)

The graph of Function A is a straight line passing through the origin (0,0) and also appears to pass through the point (4,4). The slope of a line in the form $y = mx + b$ is given by $m$, which is the "rise over run" or $\frac{\Delta y}{\Delta x}$.

Using the points (0,0) and (4,4): $\text{slope of Function A} = \frac{4 - 0}{4 - 0} = \frac{4}{4} = 1$

Function B (Table)

To find the slope of Function B, we use the given table values. We can select two points, such as (-4, -12) and (-3, -8), and calculate the slope similarly: $\text{slope of Function B} = \frac{-8 - (-12)}{-3 - (-4)} = \frac{-8 + 12}{-3 + 4} = \frac{4}{1} = 4$

Comparison

• The slope of Function A is $1$.
• The slope of Function B is $4$.

Since $1 < 4$, 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 questions?

Here are 5 related questions to expand on this concept:

1. How would the graph of Function A change if its slope were increased?
2. What happens to the line of Function B if its slope is halved?
3. How can you determine the slope of a line from a table of values?
4. Why is the slope considered the "rate of change" in linear functions?
5. How can you verify if two functions are parallel by comparing their slopes?

Tip: In linear functions, a higher slope value indicates a steeper line.