Question

Type an equation for the following pattern

Answer 1

y = -
`(2)/(3)` x + 6

Explanation:

Note the difference in consecutive terms of y is constant.

`(8)/(3)` -
`(10)/(3)` =
`(10)/(3)` - 4 = 4 -
`(14)/(3)` =
`(14)/(3)` -
`(16)/(3)` = -
`(2)/(3)`

This indicates the pattern is linear with equation

y = -
`(2)/(3)` x + b

To find b substitute any ordered pair from the table into the equation

Using (3, 4), then

4 = - 2 + b ⇒ b = 4 + 2 = 6

y = -
`(2)/(3)` x + 6 ← equation for pattern