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.

Question

1. b = 11
2. b = 12.29
3. b = 15.71
4. b = −5

Answer 1

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}.