Question

find k where y varies directly as x, and y=16 when x=8

Answer 1

"k" represents the konstant of proportionality.

If "y varies directly as x" this means that each time x increases or decreases one unit, the value of y gets modified.

How much is the modification of y each time x changes value? That is given by the constant of proportionality k.

You can express this as an equation: y= k*x

For example if k=2, you get that y=2x → meaning that each time x increases 1 unit, y will increase 2.

To calculate the value of k for given values of x and y, knowing that they vary directly you can clear it from the expression:

$\begin{gathered} y=k\cdot x \\ k=\frac{y}{x} \end{gathered}$

For x=8 and y=16

$k=\frac{y}{x}=\frac{16}{8}=2$

Then k=2 when x=8, y=16 and y varies directly as x.