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Read the description of a proportional relationship. $\newline$ In The Tall Tales of Timothy Toad, a witch brews 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), $y$ . $\newline$ After drinking $1$ milliliter of potion, the witch is invisible for $3$ minutes. Write the equation for the relationship between $x$ and $y$ . $\newline$ $y = \_\_$

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Write and solve equations for proportional relationships

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Q. Read the description of a proportional relationship.

\newline

In The Tall Tales of Timothy Toad, a witch brews 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),

y

.

\newline

After drinking

1

milliliter of potion, the witch is invisible for

3

minutes. Write the equation for the relationship between

x

and

y

.

\newline

y = \_\_

Identify given values: Step $1$ : Identify the given values: $\newline$ Amount of potion, $x = 1$ milliliter $\newline$ Time invisible, $y = 3$ minutes $\newline$ What is the constant of proportionality, $k$ ? $\newline$ Calculate $k = \frac{y}{x}$ $\newline$ $k = \frac{3}{1}$ $\newline$ $k = 3$
Calculate constant of proportionality: Step $2$ : Use the constant of proportionality to write the equation. $\newline$ Since $k = 3$ , the equation for the proportional relationship is $y = kx$ $\newline$ Thus, $y = 3x$

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