To find the initial value (or \( b \)) of the linear function, we can use the point-slope form of the equation of a line, which is:
\[ y = mx + b \]
Where:
- \( m \) is the slope (rate of change)
- \( b \) is the y-intercept (initial value)
- \( (x, y) \) is a point on the line
We are given:
- Slope \( m = -47 \)
- A point \( (14, 3) \), where \( x = 14 \) and \( y = 3 \)
Now we can plug these values into the equation and solve for \( b \):
\[ 3 = (-47)(14) + b \]
Calculate \( (-47)(14) \):
\[ -47 \times 14 = -658 \]
Now the equation becomes:
\[ 3 = -658 + b \]
Now, solve for \( b \):
\[ b = 3 + 658 \] \[ b = 661 \]
Now we need to verify if there are any options provided that correspond to the calculated value. However, it appears there may have been a misunderstanding or misinterpretation of a linear function, but based on the previous calculations, the initial value \( b \) should indeed be 661.
Since none of the options you provided include \( b = 661 \), if you meant there was an error, please double-check the given point or slope.
However, among those listed, none match. The final answer is \( b = 661 \).
If you're looking for a specific answer from the provided options, and there's context missing, please clarify what might have been entered incorrectly.