Question

A witch brewed a magical invisibility potion. There is a proportional relationship between the amount of potion the witch drinks (in milliliters), x, and the amount of time she is invisible (in minutes. After drinking 1 milliliter of potion, the witch was invisible for 5 minutes. Write the equatio for the relationship between x and y. y

Answer 1

x represents the amount of portion in millimeters

y represents the time she was invisible

Write out an equation to show the variation relationship

Since the variation is direct

Then

$\begin{gathered} x\propto y \\ x=k\times y \end{gathered}$

To get the value of k

when x= 1 mm, y = 5 minutes

$\begin{gathered} k\text{ = }\frac{x}{y} \\ =\frac{1}{5}\text{ mm/min} \end{gathered}$

The relationship between x and y will be

$\begin{gathered} \text{substitute k in x=}ky \\ x=\frac{1}{5}\times y \\ x=\frac{y}{5}\text{ (this is the relationship)} \end{gathered}$