Write a linear function that satisfies the given conditions:

f(0)=12, F(3)= -2

through points (0,12) and (3,-2)

m = slope = (-2 - 12)/ (3-0) = -14/3

12 = (-14/3)(0) + b
b = 12

y = (-14/3) x + 12
or
3 y = -14 x + 36

To write a linear function that satisfies the given conditions, we need to determine the slope (m) and the y-intercept (b).

The formula for a linear function is:
f(x) = mx + b

First, we can find the slope (m) using the given points (0, 12) and (3, -2):
m = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)

m = (-2 - 12) / (3 - 0)
m = -14 / 3

Now that we have the slope, we can substitute one of the given points (0, 12) into the equation and solve for the y-intercept (b):

12 = (-14/3)(0) + b
12 = 0 + b
b = 12

So the linear function that satisfies the given conditions is:
f(x) = (-14/3)x + 12