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Read the description of a proportional relationship. $\newline$ In a flash of sheer brilliance, Bridget invents a time machine! The machine uses a small nuclear reactor to generate the electricity it needs to travel back in time. There is a proportional relationship between how many years Bridget wants to travel back in time, $x$ , and how much electricity (in megawatts) her time machine needs, $y$ . $\newline$ To travel back $7$ years, Bridget's time machine needs $14$ megawatts of electricity. 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 a flash of sheer brilliance, Bridget invents a time machine! The machine uses a small nuclear reactor to generate the electricity it needs to travel back in time. There is a proportional relationship between how many years Bridget wants to travel back in time,

x

, and how much electricity (in megawatts) her time machine needs,

y

.

\newline

To travel back

7

years, Bridget's time machine needs

14

megawatts of electricity. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify Given Values: Step $1$ : Identify the given values: $\newline$ Years to travel back, $x = 7$ $\newline$ Electricity needed, $y = 14$ $\newline$ Calculate the constant of proportionality, $k$ . $\newline$ $k = \frac{y}{x}$ $\newline$ $k = \frac{14}{7}$ $\newline$ $k = 2$
Calculate Constant of Proportionality: Step $2$ : Use the constant of proportionality to write the equation. $\newline$ Since $k = 2$ , the equation is $y = kx$ . $\newline$ Thus, $y = 2x$

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