What is the rule in equation form of an input/output table if the inputs are 2 10 and 6 and the outputs are 2 6 and 4 ?

looks like out = in/2 + 1

To find the rule of an input/output table, we need to determine the pattern or relationship between the inputs and outputs.

Let's look at the given inputs and outputs:

Inputs: 2, 10, 6
Outputs: 2, 6, 4

First, let's look for patterns between the inputs and outputs. In this case, when the input increases by 4 (from 2 to 6), the output decreases by 2 (from 6 to 4). So, we can determine that there is a linear relationship between the inputs and outputs.

To find the rule in equation form, we need to determine the equation based on the pattern we identified.

Let's consider the equation form: y = mx + b

Here, y represents the output, x represents the input, m represents the slope, and b represents the y-intercept.

Using the first pair of inputs and outputs (2, 2), we can substitute the values into the equation:

2 = m(2) + b

Simplifying, we have:

2 = 2m + b

Using the second pair of inputs and outputs (10, 6), we can substitute the values into the equation:

6 = m(10) + b

Simplifying, we have:

6 = 10m + b

Now we have a system of equations:

2 = 2m + b (Equation 1)
6 = 10m + b (Equation 2)

To find the values of m and b, we can solve this system of equations simultaneously.

Subtracting Equation 1 from Equation 2, we get:

6 - 2 = 10m - 2m + b - b

4 = 8m

Dividing both sides of the equation by 8, we have:

m = 4/8
m = 0.5

Now, substituting the value of m into Equation 1, we can solve for b:

2 = 2(0.5) + b

2 = 1 + b

Subtracting 1 from both sides, we get:

1 = b

Therefore, the rule in equation form for this input/output table is:

y = 0.5x + 1