https://file.aiquickdraw.com/mathbot/file/1726441494016hlo7fvuj.jpg

Let's analyze the given functions and answer the questions based on the image.

We have four functions to consider:

1. **Function 1**: Information missing in the visible part.
2. **Function 2**: Information missing in the visible part.
3. **Function 3**: \( y = 2x + 5 \) (slope = 2, y-intercept = 5).
4. **Function 4**: The slope is \( -1 \) and the y-intercept is \( -4 \).

Now, let's answer each question:

### (a) Which function's graph is the least steep?
- The steepness of a line is determined by the absolute value of the slope. The smaller the absolute value, the less steep the graph is.
  - **Function 3** has a slope of 2.
  - **Function 4** has a slope of \( -1 \), which has an absolute value of 1.

  Therefore, **Function 4** is the least steep because \( | -1 | = 1 \) is smaller than 2.

### (b) Which functions have graphs with slopes less than \( -2 \)?
- The condition is that the slope should be less than \( -2 \). None of the visible slopes (2 and -1) meet this criterion.
  - **Function 3** has a slope of 2 (greater than -2).
  - **Function 4** has a slope of \( -1 \) (greater than -2).

  So, none of the visible functions (Function 3 or Function 4) have slopes less than \( -2 \).

### (c) Which function has the graph with the greatest y-intercept?
- The y-intercept is where the graph crosses the y-axis (when \( x = 0 \)).
  - **Function 3** has a y-intercept of 5.
  - **Function 4** has a y-intercept of \( -4 \).

  Since 5 is greater than \( -4 \), **Function 3** has the greatest y-intercept.

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Would you like further details on this or to clarify anything? Here are 5 related questions you might find helpful:

1. What is the relationship between slope and steepness in linear functions?
2. How do you find the slope of a line given two points?
3. Can the y-intercept affect the steepness of a graph?
4. How do positive and negative slopes affect the direction of a line?
5. How can we graph a line given the slope and y-intercept?

**Tip**: Always remember that the slope of a line determines both its steepness and direction. The greater the absolute value of the slope, the steeper the line!

Which function's graph is the least steep? Which functions have graphs with slopes less than -2? Which function has the graph with the greatest y-intercept?

Learn how to determine which linear function has the least steep graph, identify functions with slopes less than -2, and find the graph with the greatest y-intercept. This problem involves linear equations and the relationship between slope and y-intercept. Suitable for Grades 8-10.

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