What is the slope of this relation:

**x**

**y**

0

22

2

16

4

10

6

4

8

-2




To determine the slope of the given relation, we need to find the change in \( y \) divided by the change in \( x \). This is typically done using the formula for slope, \( m \), which is:

\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]

We can pick any two points from the given data to calculate the slope. Let's use the first two points \((0, 22)\) and \((2, 16)\):

\[ m = \frac{16 - 22}{2 - 0} = \frac{-6}{2} = -3 \]

To confirm, we can check with other points to ensure consistency. Using the points \((2, 16)\) and \((4, 10)\):

\[ m = \frac{10 - 16}{4 - 2} = \frac{-6}{2} = -3 \]

The slope remains consistent, and calculating with the points \((4, 10)\) and \((6, 4)\):

\[ m = \frac{4 - 10}{6 - 4} = \frac{-6}{2} = -3 \]

Finally, verifying with the points \((6, 4)\) and \((8, -2)\):

\[ m = \frac{-2 - 4}{8 - 6} = \frac{-6}{2} = -3 \]

Since the slope is consistently \(-3\) for all pairs of points, we can confidently state that the slope of this relation is \( -3 \).

Would you like further details or have any questions?

Here are 5 questions you might want to ask next:
1. How do you interpret the slope of -3 in a real-world context?
2. Can you find the equation of the line that fits this data?
3. What is the y-intercept of the line that fits this data?
4. How can you determine if a set of points lies on a straight line?
5. What are some applications of finding the slope in real life?

**Tip:** Always verify the slope calculation using multiple points to ensure consistency and accuracy in your results.

Discover how to calculate the slope of a linear relation using points. This problem features points (0, 22), (2, 16), (4, 10), (6, 4), and (8, -2), resulting in a consistent slope of -3. Ideal for students in Grades 6-8.

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