To solve this problem, we need to analyze the graphs and compare the slopes of the lines in the four figures (A, B, C, D).

Key Concepts:

• The slope of a line is the rate at which it rises or falls, which is calculated as the ratio of the "change in y" (vertical change) to the "change in x" (horizontal change).
• Positive slopes mean the line rises as you move from left to right, and negative slopes mean the line falls. A slope of zero means the line is horizontal, and undefined (very steep) lines have no slope.

Analyzing the slopes:

1. Graph A: This line is falling as you move from left to right, which indicates a negative slope.
2. Graph B: The line is perfectly horizontal, which gives it a slope of 0.
3. Graph C: This line is rising as you move from left to right, indicating a positive slope, and it seems relatively steep.
4. Graph D: Similar to graph C, this line is rising, but it's less steep than the line in C, meaning it has a smaller positive slope.

Ordering by increasing slope:

• The smallest slope is in Graph A because it is negative.
• Next, Graph B has a slope of 0.
• Then comes Graph D, with a small positive slope.
• Finally, Graph C has the steepest positive slope.

Correct order:

The graphs in order of increasing slope are: A, B, D, C.

Would you like further details on how slope is calculated, or do you have any questions? Here are 5 related questions to deepen your understanding:

1. How do you calculate the slope of a line given two points?
2. What does a negative slope tell you about a line’s behavior?
3. Can a vertical line have a slope? Why or why not?
4. How does changing the slope affect the steepness of the line?
5. What is the difference between the slope of a horizontal and a vertical line?

Tip: Remember, a larger positive slope means a steeper rise, while a negative slope indicates a decline.