Question

Find a and b given f(x) = ax + b, f(1) = 7, and f(3) = -5.

Answer 1

Answer:

a = - 6, b = 13

Step-by-step explanation:

Given f(1) = 7 , that is f(x) = 7 when x = 1

f(3) = - 5 , that is f(x) = - 5 when x = 3

Substitute these values into f(x) = ax + b

a + b = 7 → (1)

3a + b = - 5 → (2)

Subtract (1) from (2) term by term to eliminate b

(3a - a) + (b - b) = - 5 - 7

2a = - 12 ( divide both sides by 2 )

a = - 6

Substitute a = - 6 into either of the 2 equations and solve for b

Substituting into (1)

- 6 + b = 7 ( add 6 to both sides )

b = 13