What's the value of f(6)?

Question

f(x)=ax+b

 

In the function above a and b are constants. If f(0)=3 and f(3)=-8, what's the value of f(6)?

Answer 1

Notice the initial value condition   f(0)=3   is the y-intercept.  So your value of b is 3.  So far, your equation is

 

f(x) = ax + 3

 

Next, we find to find the value of a.  This is the slope between the two points: (0, 3) and (3, -8). 

 

a = (-8 - 3) / (3 - 0)

a = -11/3

 

So your function will be

 

f(x) = (-11 / 3)x + 3

 

Next, evaluate this function when x=6 to find f(6).

Answer 2

Since f(0) = 3, a(0) + b = 3.  So, b = 3

 

Therefore, f(x) = ax + 3

 

Since f(3) = -8, a(3) + 3 = -8

 

                      3a + 3 = -8

 

                            3a = -11    a = -11/3

 

So, f(x) = (-11/3)x + 3

 

Thus, f(6) = (-11/3)(6) + 3 = -19