To find the initial value (y-intercept) \( b \) of the linear function, you can use the slope-intercept form of the equation of a line, which is given by:
\[ y = mx + b \]
In this case, you have:
- The slope \( m = -47 \)
- A point on the line \( (x, y) = (14, 3) \)
You can substitute the values into the equation to solve for \( b \).
\[ 3 = -47(14) + b \]
Calculating \( -47(14) \):
\[ -47 \times 14 = -658 \]
Now substitute that back into the equation:
\[ 3 = -658 + b \]
To isolate \( b \), add 658 to both sides:
\[ b = 3 + 658 = 661 \]
Now, I realize that the options you provided don't include 661. Let's double-check the calculations but based on our current findings, we have not matched those values. If you had a mistake in the values or if the slope was different, it could lead to re-evaluation.
Let's go through it briefly:
- Initial values substituted should give a correct slope intercept if done accurately.
- Your point determines its position along with slope to ultimately yield the y-intercept.
Given that none of the answer options match what's been calculated, could you please check the values provided again?
However, if confirmed, the function would require further context or corrections in selection options provided.