Question

Determine if y varies with x. and if so find the constant variation of k and write the equation

Answer 1

Suppose y varies directly as x then we have

`y\propto x`

This implies

`y=kx`

Where k is a constant of variation

From the table

When x = 7, y = 11

This implies

`\begin{gathered} 11=7k \\ k=(11)/(7) \end{gathered}`

We need to check if the value of k satisfy other pairs of x and y

From the table

when x = 8, y = 13

Using the value of k

we have

`13=(11)/(7)*8`

But this equation is not true because the LHS is not equal to RHS

That is

`13\\e(11)/(7)*8`

Hence the value of k is not unique for the given values of x and y

Therefore, y does not vary directly with x