Explain how to write a function rule from table below. then write function rule.

(x) 2, 4, 6

(y) 1, 0, -1

The linear equation describing the given table is y = (-1/2)x + 2.

Step-by-step explanation:

Let's assume that this is a linear function.

As we go from x = 2 to x = 4, (an increase of 2), y goes from 1 to 0 (a decrease of -1).  Thus, the slope of the line is m = rise / run = -1/2.

Borrowing info from the table:  when x = 4, y = 0.

Thus, y = mx + b becomes 0 = (-1/2)(4) + b, so that b = 2.

The linear equation describing the given table is y = (-1/2)x + 2.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2