Find the initial value of the linear function, given that the rate of change is m = −47, and (14, 3) is an (x, y) value of the linear function.
1. b = 11
2. b = 12.29
3. b = 15.71
4. b = −5
Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1)
where m = -47, x1 = 14, and y1 = 3. Substituting these values, we get:
y - 3 = -47(x - 14)
Simplifying and rearranging, we get:
y = -47x + 665
The initial value is the y-intercept, which occurs when x = 0. Therefore, we substitute x = 0 into the equation and solve for y:
y = -47(0) + 665
y = 665
So the initial value of the linear function is b = 665. Answer: \boxed{3}.