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To find the initial value of the linear function, we need to use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substitute m = -4/7, x1 = 14, and y1 = 3 into the equation:
y - 3 = (-4/7)(x - 14)
y - 3 = (-4/7)x + 8
y = (-4/7)x + 11
Now, since the initial value is the y-intercept of the linear function, we need to find the value of y when x = 0:
y = (-4/7)(0) + 11
y = 11
Therefore, the initial value of the linear function is 11.