Question

Write a function rule for

X

Y

-1

4

1

0

2

-2

M = ___
B = ___
Function Rule: ____

Answer 1

To find the function rule \( Y = MX + B \) based on the given points, we can use the points to determine the slope \( M \) and y-intercept \( B \).

### Given Points:
- Point 1: \( (-1, 4) \)
- Point 2: \( (1, 0) \)
- Point 3: \( (2, -2) \)

### Step 1: Calculate the Slope (M)
The slope \( M \) can be calculated using any two points. Let's use the first two points \( (-1, 4) \) and \( (1, 0) \).

The formula for the slope \( M \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
M = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in our values:

\[
M = \frac{0 - 4}{1 - (-1)} = \frac{-4}{2} = -2
\]

### Step 2: Calculate the Y-intercept (B)
We'll use the slope and one of the points to find the y-intercept \( B \). We can use the point \( (1, 0) \):

The linear equation can be rearranged to find \( B \):

\[
Y = MX + B \implies B = Y - MX
\]

Substituting the values:

\[
0 = -2(1) + B \implies B = 0 + 2 = 2
\]

### Final Function Rule:
We can represent the function rule as:

\[
Y = -2X + 2
\]

### Summary:
- \( M = -2 \)
- \( B = 2 \)
- **Function Rule**: \( Y = -2X + 2 \)