To find the initial value (y-intercept) \( b \) of the linear function, we can use the slope-intercept form of the linear equation, which is given by:
\[ y = mx + b \]
Here, \( m \) is the slope (rate of change) and \( (x, y) \) is a point on the line. We can rearrange this equation to solve for \( b \) using the provided point \( (14, 3) \) and the slope \( m = -47 \).
Using the point \( (14, 3) \):
- Substitute \( y = 3 \), \( m = -47 \), and \( x = 14 \) into the equation:
\[ 3 = -47(14) + b \]
- Calculate \( -47(14) \):
\[ -47 \times 14 = -658 \]
- Now substitute that value back into the equation:
\[ 3 = -658 + b \]
- To solve for \( b \), add 658 to both sides:
\[ b = 3 + 658 \]
- Therefore,
\[ b = 661 \]
Given the options you've provided, it seems there might be a misunderstanding as we arrived at 661, which is not one of the choices. Please double-check the values given or the slope to ensure everything is correct, or let me know if there is any additional information.