Answer:
see explanation
Step-by-step explanation:
Expressing the rule in the form y = mx + b
where m is the slope and b the y- intercept
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (4, 0) ← 2 ordered pairs from the table
m = [tex]\frac{0-1}{4-2}[/tex] = [tex]\frac{-1}{2}[/tex] = - [tex]\frac{1}{2}[/tex], thus
y = - [tex]\frac{1}{2}[/tex] x + b ← is the partial equation
To find b substitute any ordered pair into the partial fraction
Using (4, 0), then
0 = - 2 + b ⇒ b = 0 + 2 = 2
y = - [tex]\frac{1}{2}[/tex] x + 2 ← function rule
