find the initinal 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.
To find the initial value of the linear function, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substitute the given values m = -4/7, x1 = 14, and y1 = 3:
y - 3 = (-4/7)(x - 14)
Next, we can simplify the equation:
y - 3 = (-4/7)x + 56/7
y = (-4/7)x + 56/7 + 3
y = (-4/7)x + 56/7 + 21/7
y = (-4/7)x + 77/7
y = (-4/7)x + 11
Now, we can see that the initial value (y-intercept) of the linear function is 11.