4th grade function tables with 2 variables

Input output
5 12
8 24
11 36
14 48

To find the relationship between the input and the output in a function table with 2 variables, we need to look for a pattern or rule.

In this case, we can observe that as the input increases by 3 (from 5 to 8, 8 to 11, and 11 to 14), the output increases by 12 (from 12 to 24, 24 to 36, and 36 to 48). This suggests that there is a constant rate of change, or slope, between the input and the output.

To determine the rule, we can calculate the slope by finding the difference in the outputs divided by the difference in the inputs. Let's take the first two data points as an example:

Slope = (output_2 - output_1) / (input_2 - input_1)
Slope = (24 - 12) / (8 - 5)
Slope = 12 / 3
Slope = 4

Now that we have the slope, we can determine the rule for the function table. We can express it using the equation:

Output = Slope * Input + Constant

To find the constant, we can substitute the slope and any input and output values into the equation. Let's use the first data point:

12 = 4 * 5 + Constant
12 = 20 + Constant
Constant = 12 - 20
Constant = -8

Therefore, the rule for the function table is:

Output = 4 * Input - 8

We can verify the rule by checking if it holds true for the other data points:

8 = 4 * 8 - 8
8 = 32 - 8
8 = 24 (True)

11 = 4 * 11 - 8
11 = 44 - 8
11 = 36 (True)

14 = 4 * 14 - 8
14 = 56 - 8
14 = 48 (True)

So, the rule Output = 4 * Input - 8 applies to all the given input-output pairs in the function table.