Suppose f(0)= 4 and f(3)= 8.Find f(12)if f is a linear function.
A) -3
B) 6
C) 13
D) 20
E) 24

Question

Quizplus · Accepted Answer

Since f is a linear function, it has the form f(x) = mx + b, where m is the slope and b is the y-intercept. We are given two points on the line: (0,4) and (3,8).

Using these points, we can compute the slope:

m = (8-4)/(3-0) = 4/3

Now we can use the slope and one of the points to find the y-intercept:

4 = (4/3)(0) + b

b = 4

So the linear function is:

f(x) = (4/3)x + 4

To find f(12), we simply plug in x = 12:

f(12) = (4/3)(12) + 4 = 20

Therefore, the answer is D) 20.

Suppose F(0)= 4 and F(3)= 8