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Read the description of a proportional relationship. $\newline$ Tom and his friends set out to sea on their annual fishing trip. There is a proportional relationship between the time (in hours) Tom and his friends spend sailing, $x$ , and their distance from shore (in miles), $y$ . $\newline$ After sailing for $1$ hour, they are $5$ miles from shore. 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

Tom and his friends set out to sea on their annual fishing trip. There is a proportional relationship between the time (in hours) Tom and his friends spend sailing,

x

, and their distance from shore (in miles),

y

.

\newline

After sailing for

1

hour, they are

5

miles from shore. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify values & relationship: Identify the given values and the relationship type. We know that after $1$ hour of sailing, they are $5$ miles from shore. This sets up a direct proportion between time and distance.
Calculate constant of proportionality: Calculate the constant of proportionality, $k$ . Since $y = kx$ and we know $y = 5$ when $x = 1$ , we can solve for $k$ by dividing the distance by the time. $k = \frac{5 \text{ miles}}{1 \text{ hour}} = 5$ .
Write equation with constant: Write the equation using the constant of proportionality. Since $k = 5$ , the equation relating time and distance is $y = 5x$ .

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