Question

Write a function rule for

X

Y

1

5

2

4

3

3

4

2

5

1

M = ___
B = ___
Function Rule: ____

Answer 1

To find the function rule that describes the relationship between X and Y based on the provided data, we first need to analyze the data points:

```
X | Y
-----
1 | 5
2 | 4
3 | 3
4 | 2
5 | 1
```

From observing the Y values as X increases, we can see that Y decreases. Specifically, as X increases by 1, Y decreases by 1. This suggests a linear function where Y is decreasing as X increases.

The pattern of the data can be represented in the form of a linear equation:

\[ Y = MX + B \]

### Finding M and B:

1. **Slope (M)**: Determine how much Y changes with respect to X.
- When X increases from 1 to 2, Y decreases from 5 to 4, which is a change of -1.
- This pattern continues consistently for each step. Therefore, the slope (M) is -1.

2. **Y-Intercept (B)**: This is the value of Y when X = 0. To find B, we can use one of the points. Let's use the first point (1, 5):
- Plugging X = 1 and Y = 5 into the equation \( Y = MX + B \):
\[
5 = -1(1) + B
\]
\[
5 = -1 + B
\]
\[
B = 5 + 1 = 6
\]

### Conclusion:

- M = -1
- B = 6
- Therefore, the function rule is:

\[ Y = -1X + 6 \]

In summary:
- M = -1
- B = 6
- Function Rule: \( Y = -1X + 6 \)