Answer:
y = [tex]\frac{1}{2}[/tex] x
Step-by-step explanation:
The equation of a linear pattern has the form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, [tex]\frac{1}{2}[/tex] ) and (x₂, y₂ ) = (2, 1) ← 2 ordered pairs from the table
m = [tex]\frac{1-\frac{1}{2} }{2-1}[/tex] = [tex]\frac{1}{2}[/tex] , thus
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c use any ordered pair from the table and substitute into the partial equation.
Using (2, 1) , then
1 = 1 + c ⇒ c = 1 - 1 = 0
y = [tex]\frac{1}{2}[/tex] x + 0 ← equation for pattern or quite simply
y = [tex]\frac{1}{2}[/tex] x
