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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?

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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.

Four different linear functions are represented below. (a) Which function's graph is the least steep? (b) Which function has the graph with the greatest y-intercept? (c) Which functions have graphs with slopes less than -3? (Check all that apply.)

Learn how to analyze linear functions by comparing slopes and y-intercepts. This problem focuses on determining which graph is the least steep, finding the graph with the greatest y-intercept, and identifying functions with slopes less than -3. Suitable for students in Grades 8-10.

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