Explain how to write a function rule from the table below. Then write a function rule.

x 2 4 6
y 1 0 –1

y = mx + b

f(x) = 2m + b = 1
f(x) = 4m + b = 0
f(x) = 6m + b = -1

-1(2m + b = 1)
4m + b = 0

-2m -b = -1
4m + b = 0

2m = -1
m = -1/2
2(-1/2) + b = 1
-1 + b = 1
-1+ 1 + b = 1 + 1
b = 2
y = mx +b
y = -1/2x + 2

To write a function rule from a given table, we need to understand the relationship between the input values (x) and the corresponding output values (y).

In this table:
x: 2, 4, 6
y: 1, 0, -1

To determine the function rule, we need to observe how the input (x) relates to the output (y). Let's examine the given data:

When x increases by 2, y decreases by 1.
When x increases by 2, y decreases by 1.
When x increases by 2, y decreases by 1.

From this pattern, we can conclude that for every increase of 2 in x, y decreases by 1.

Therefore, the function rule for this table can be written as:

y = -1*x/2

Explanation: The function rule y = -1*x/2 indicates that the output y is computed by taking the input x, multiplying it by -1, and then dividing the result by 2. This rule follows the pattern observed in the table.