https://file.aiquickdraw.com/mathbot/file/1728536028168ad7f3chd.jpg

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.

Order the following graphs by increasing slope of the line being displayed (WW 2a Section 2 Linear Functions: Problem 9).

Solve the problem of ordering graphs by increasing slope. This problem focuses on linear functions and the concept of slope, suitable for students in Grades 8-10. Learn how to compare slopes of lines visually.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation