To find the equation of the linear function with a slope of -3 that passes through the point (-2, 9), we can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.
Given:
- Slope \( m = -3 \)
- Point \( (x_1, y_1) = (-2, 9) \)
Substituting these values into the point-slope form:
\[ y - 9 = -3(x - (-2)) \] \[ y - 9 = -3(x + 2) \]
Now, distribute the -3:
\[ y - 9 = -3x - 6 \]
Next, isolate \( y \):
\[ y = -3x - 6 + 9 \] \[ y = -3x + 3 \]
Now we can match this equation with the options provided.
The function we found is: \[ y = -3x + 3 \]
Looking at the provided options:
- \( Y = -3x + 3 \) (This is the correct answer)
- \( Y = -2x - 3 \)
- \( Y = -3x + 9 \)
- \( Y = 3x - 3 \)
Thus, the matching linear function is \( Y = -3x + 3 \).