Let's analyze each function based on the provided information:

Function 1:

• This is the graph in the top-left quadrant.
• The slope appears to be positive and relatively steep.

Function 2:

• Given as a table with points $(-2, 9)$, $(-1, 4)$, $(0, -1)$, $(1, -6)$, and $(2, -11)$.
• To find the slope, use any two points: $\text{slope} = \frac{-6 - (-1)}{1 - 0} = \frac{-5}{1} = -5$ The slope is $-5$.

Function 3:

• $y = -2x + 5$
• The slope is $-2$.

Function 4:

• The slope is $1$ and the $y$-intercept is $2$.
• Equation: $y = x + 2$.

Now let's answer the questions:

(a) Which function's graph is the least steep?

• Steepness relates to the absolute value of the slope.
• Slopes: Function 1 (unknown but positive), Function 2 ($-5$), Function 3 ($-2$), Function 4 ($1$).
• The least steep graph corresponds to the smallest absolute slope. $\text{Answer: Function 4 (slope = 1)}$

(b) Which function has the graph with the greatest $y$-intercept?

• $y$-intercepts:
  • Function 1 (unclear but appears positive),
  • Function 2 ($-1$ when $x = 0$),
  • Function 3 ($5$ when $x = 0$),
  • Function 4 ($2$ when $x = 0$).
  • The greatest $y$-intercept is $5$. $\text{Answer: Function 3}$

(c) Which functions have graphs with slopes less than $-3$?

• Slopes less than $-3$:
  • Function 2 ($-5$) is less than $-3$. $\text{Answer: Function 2}$

Do you need any further details or have any questions?

Here are 5 relative questions to expand on this topic:

1. How does the steepness of a graph relate to the magnitude of the slope?
2. How can you determine the slope from a graph directly?
3. What role does the $y$-intercept play in graphing linear functions?
4. How can we derive the equation of a line from two points?
5. What is the significance of a positive versus negative slope in a graph?

Tip: Remember that the slope tells you how much the $y$-value changes for each unit increase in $x$. The greater the absolute value of the slope, the steeper the line.