Answer:
see explanation
Step-by-step explanation:
This is a linear pattern with the equation in the form
y = mx + c
To find m use the points (2, 9) and (4, 6) and the formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
m = [tex]\frac{6-9}{4-2}[/tex] = [tex]\frac{-3}{2}[/tex] = - [tex]\frac{3}{2}[/tex], thus
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute any ordered pair from the table into the partial equation.
Using (2, 9), then
9 = - 3 + c ⇒ c = 9 + 3 = 12
y = - [tex]\frac{3}{2}[/tex] x + 12 ← equation for pattern
