Determine the relationship between the input and output: \begin{tabular}{|c|c|} \hline Input & Output \\ \hline 25 & 15 \\ \hline 30 & 18 \\ \hline 35 & 21 \\ \hline 40 & 24 \\ \hline \end{tabular}

Step 1 ：Observe the given table and notice that the output seems to be increasing by 3 as the input increases by 5. This suggests a linear relationship between the input and output.

Step 2 ：Calculate the slope of the line that these points would form on a graph. The slope is the change in output divided by the change in input, which in this case is 3/5 or 0.6. This means that for every increase of 1 in the input, the output increases by 0.6.

Step 3 ：However, this doesn't give us the exact output values in the table, so there must also be a constant term in the relationship. To find this, subtract the product of the slope and a known input from the corresponding output. For example, using the first row of the table, 15 - 0.6*25 = -15.

Step 4 ：This suggests that the relationship is output = 0.6*input - 15.

Step 5 ：Test the function with the given inputs to confirm. The function correctly calculates the output for all given inputs. This confirms that the relationship is indeed output = 0.6*input - 15.

Step 6 ：Final Answer: The relationship between the input and output is given by the equation \(\boxed{output = 0.6*input - 15}\).