Question

Find a equation for the following pattern! Help!!!

Answer 1

y =
`(1)/(2)` x

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 =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (1,
`(1)/(2)` ) and (x₂, y₂ ) = (2, 1) ← 2 ordered pairs from the table

m =
`(1-(1)/(2) )/(2-1)` =
`(1)/(2)` , thus

y =
`(1)/(2)` 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 =
`(1)/(2)` x + 0 ← equation for pattern or quite simply

y =
`(1)/(2)` x