https://file.aiquickdraw.com/mathbot/file/17272171135837slfkybp.jpg

The image shows a graph of lines and triangles with points labeled A, B, C, D, E, and F. Below the graph, there are two questions related to finding the slopes of line segments:

1. **Question: "Find the slope of AC."**
   The slope between two points is calculated using the formula:
   \[
   \text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   In this case, points A and C are:
   - A (7, 0)
   - C (0, 7)

   Applying the slope formula:
   \[
   \text{slope of AC} = \frac{7 - 0}{0 - 7} = \frac{7}{-7} = -1
   \]
   So, the slope of AC is \(-1\).

2. **Question: "Which is a true statement about the slope of AC compared to the slope of DF?"**
   - To answer this, we first need the slope of DF. Points D and F are:
     - D (4, 3)
     - F (0, 1)

   Applying the slope formula:
   \[
   \text{slope of DF} = \frac{1 - 3}{0 - 4} = \frac{-2}{-4} = \frac{1}{2}
   \]

   So, the slope of DF is \(\frac{1}{2}\). Now comparing:
   - The slope of AC is \(-1\), and the slope of DF is \(\frac{1}{2}\).
   - \(-1\) is less than \(\frac{1}{2}\), so the true statement is: 
     \[
     \text{The slope of AC is less than the slope of DF.}
     \]

Let me know if you want more details or have any questions! Here are 5 related questions:

1. How do you find the slope between any two points?
2. Why is the slope of a vertical line undefined?
3. Can two different lines have the same slope but never intersect? Why or why not?
4. What is the significance of a positive vs. negative slope in a graph?
5. How do the slopes of perpendicular lines relate to each other?

**Tip:** Always check the coordinates carefully when calculating slopes—small errors can lead to incorrect conclusions!

Find the slope of AC and compare it with the slope of DF.

Learn how to find the slopes of line segments AC and DF using the slope formula. This problem demonstrates key concepts in coordinate geometry and is suitable for students in Grades 7-9.

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