To find the initial value (b) of the linear function, we can use the point-slope formula which states that the equation of a linear function can be written as y = mx + b, where m is the rate of change and b is the initial value.
Given that m = -47 and (14,3) is a point on the line, we can substitute these values into the equation to solve for b:
3 = -47(14) + b
Simplifying the equation:
3 = -658 + b
To isolate b, we can add 658 to both sides of the equation:
3 + 658 = b
661 = b
Therefore, the initial value (b) of the linear function is 661.
So, the correct answer is: b = 661.