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Read the description of a proportional relationship. $\newline$ Maggie's space shuttle crew accidentally left her behind on a mysterious planet. She soon realizes that her body is aging much faster on this planet than it did on Earth. There is a proportional relationship between the number of weeks Maggie spends on the planet, $x$ , and the number of years she ages, $y$ . $\newline$ After $3$ weeks on the planet, Maggie's body has aged $12$ years. 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

Maggie's space shuttle crew accidentally left her behind on a mysterious planet. She soon realizes that her body is aging much faster on this planet than it did on Earth. There is a proportional relationship between the number of weeks Maggie spends on the planet,

x

, and the number of years she ages,

y

.

\newline

After

3

weeks on the planet, Maggie's body has aged

12

years. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify Given Values: Step $1$ : Identify the given values from the problem description. $\newline$ Maggie spends $x = 3$ weeks on the planet and ages $y = 12$ years. We need to find the constant of proportionality, $k$ . $\newline$ Calculate $k$ using the formula $k = \frac{y}{x}$ . $\newline$ $k = \frac{12}{3}$ $\newline$ $k = 4$
Calculate Constant of Proportionality: Step $2$ : Use the constant of proportionality to write the equation for the proportional relationship. $\newline$ Since $k = 4$ , the equation relating the number of weeks ( $x$ ) and the number of years aged ( $y$ ) is $y = kx$ . $\newline$ Thus, $y = 4x$

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