Question

Write a linear function f with f(-4) = 2 and f(6) =-3​

Answer 1

Answer:

f(x) = - $\frac{1}{2}$ x

Step-by-step explanation:

The standard form for a linear function is

f(x) = ax + b

Using the given values f(- 4) = 2 and f(6) = 3 , then

- 4a + b = 2 → (1)

6a + b = - 3 → (2)

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

- 10a = 5 ( divide both sides by - 10 )

a = - $\frac{1}{2}$

Substitute a = - $\frac{1}{2}$ into either of the 2 equations and solve for b

Substituting into (1)

2 + b = 2 ( subtract 2 from both sides )

b = 0

Thus the linear function is

f(x) = - $\frac{1}{2}$ x