To find the initial value (y-intercept) \( b \) of the linear function given the slope \( m = -47 \) and the point \( (14, 3) \), we can use the point-slope form of the linear equation:
\[ y - y_1 = m(x - x_1) \]
Where \( (x_1, y_1) \) is the point \( (14, 3) \). Plugging in the values, we have:
\[ y - 3 = -47(x - 14) \]
Expanding this equation:
\[ y - 3 = -47x + 658 \]
Adding 3 to both sides to isolate \( y \):
\[ y = -47x + 658 + 3 \] \[ y = -47x + 661 \]
The y-intercept \( b \) is the constant term when the equation is in the form \( y = mx + b \). Therefore,
\[ b = 661 \]
None of the provided options match \( b = 661 \). Please check the options again, as there seems to be some inconsistency. However, based on the given information, the correct calculation is:
b = 661.