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

$\begin{gathered} 11=7k \\ k=\frac{11}{7} \end{gathered}$

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

$13=\frac{11}{7}\times8$

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

That is

$13\ne\frac{11}{7}\times8$

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

Therefore, y does not vary directly with x