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

The linear function is f(x) = -0.5x

For f(-4) = 2

x₁ = -4, y₁ = 2

For f(6) = -3

x₂ = 6, y₂ = -3

The slope(m) is found using the formula

m = (y₂ - y₁)/(x₂ - x₁)

m = (-3-2)/(6-(-4))

m = -5/10

m = -0.5

Substitute m = -0.5, x₁= -4, and y₁ = 2 into the equation below:

y - y₁ = m(x - x₁)

y - 2 = -0.5(x - (-4))

y - 2 = -0.5(x + 4)

y - 2 = -0.5x - 2

y = -0.5x - 2 + 2

y = -0.5x

Therefore, the linear function is f(x) = -0.5x

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f(x) = - 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 = -

Substitute a = - 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) = - x

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

answer: sine

step-by-step explanation: