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

answer: c.  

step-by-step explanation:

mixtures containing substances that get attracted to magnet can be separated using a magnet. we can separate iron from a mixture of sand and iron, as only iron attracts to the magnet.