Answer:
f(x) = - [tex]\frac{1}{2}[/tex] 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 = - [tex]\frac{1}{2}[/tex]
Substitute a = - [tex]\frac{1}{2}[/tex] 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) = - [tex]\frac{1}{2}[/tex] x
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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