Question

MARKNING BRAINLEST ! :) * The table shows a linear function, find the values of A , B , & C. Show your work.

Answer 1

Answer:

A = 11, B = 25/3, C = -1

Step-by-step explanation:

A linear function has the form:

f(x) = ax + b

(1)

f(3) = 8a + b = 8

f(5) = 5a + b = 9

Using the last 2 equations we can solve for 'a' and 'b'.

8a + b = 8 | 5a + b = 9

We multiply the second one by -1:

8a + b = 8 | -5a -b = -9

And then we add them together:

3a = -1

a = $\frac{-1}{3}$

We then solve for 'b':

5a + b = 9

5(-1/3) + b = 9

b = 9 + 5/3

b = 32/3 = $11\frac{1}{3}$.

We then use this to find A, B, C.

f(x) = (-1/3)x + 32/3

(2)

f(A) = -A/3 + 32/3 = 7

$\frac{-A}{3} + \frac{32}{3} = 7\\A - 32 = -21\\A = 11$

(3)

f(7) = -7/3 + 32/3 = B

25/3 = B

(4)

f(C) = -C/3 + 32/3 = 11

$\frac{-C}{3} + \frac{32}{3} = 11\\C - 32 = -33\\C = -1$