Find the initial value of the linear function, given that the rate of change is m = −4/7, 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:
y - y1 = m(x - x1)
Substituting in the given values:
y - 3 = (-4/7)(x - 14)
Simplifying:
y - 3 = (-4/7)x + 8
y = (-4/7)x + 11
The initial value (y-intercept) of this linear function is b = 11, so the correct answer is 1. b = 11.