Question

Find the linear function formula f(x) = mx + b for the function described:A) f(0) =10 and m= -2/3B) f(1)=5 and m=3C) f(2)=6 and f(4)=0D) f(3) =4 and f(6)= -3E) f(0) =8 and f(x) decreases by 2 when x increases by 3

Answer 1

Answer:

A.

f(x) = (-2/3)x + 10

B.

f(x) = 3x + 2

C.

f(x) = -3x - 12

Step-by-step explanation:

A.

For f(0) = 10 and m = -2/3

Put x = 0 and m = -2/3

10 = (-2/3)(0) + b

b = 10

f(x) = (-2/3)x + 10

B.

f(1) = 5 and m = 3

Put x = 1 and m = 3 to obtain b

5 = 3(1) + b

b = 5 - 3 = 2

f(x) = 3x + 2

C.

f(2) = 6 and f(4) = 0

Put x = 2 and f(x) = 6, also x = 4 and f(x) = 0

6 = 2m + b............................(1)

0 = 4m + b............................(2)

Solving (1) and (2) simultaneously

(2) - (1)

-6 = 2m

m = -6/2 = -3

Using m = -3 in (2)

0 = 4(-3) + b

b = -12

Therefore, we have m = -3 and b = -12

Putting these in the given equation

f(x) = -3x - 12