Question

What is the function/equation for the input/output table? xy 324 243 202.5 162options:y = 8 - xy = 8 xy = x - 1y = x\8

Answer 1

`y=(x)/(8)`

Step-by-step explanation

We want to find the equation of the input/output table.

Notice from the table that each value of y is smaller than each value of x by a multiplicative factor. This implies that x and y have a proportional relationship:

`y=kx`

where k = constant of proportionality

To find the constant of proportionality, substitute a pair of x and y values from the table into the equation.

Let us use (24, 3):

`\begin{gathered} 3=k*24 \\ \\ k=(3)/(24) \\ \\ k=(1)/(8) \end{gathered}`

Therefore, the equation for the table is:

`\begin{gathered} y=(1)/(8)*x \\ \\ y=(x)/(8) \end{gathered}`

That is the correct answer.