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Read the description of a proportional relationship. $\newline$ Anthony has written his own recipe for pot roast. There is a proportional relationship between the weight (in pounds) of the pot roast, $x$ , and the total cooking time (in hours), $y$ . $\newline$ His recipe says that a $5$ -pound roast should take $2$ hours to cook. 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

Anthony has written his own recipe for pot roast. There is a proportional relationship between the weight (in pounds) of the pot roast,

x

, and the total cooking time (in hours),

y

.

\newline

His recipe says that a

5

-pound roast should take

2

hours to cook. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify Constant of Proportionality: Step $1$ : Identify the constant of proportionality from the given values. $\newline$ Given: $5$ pounds of roast takes $2$ hours to cook. $\newline$ To find the constant of proportionality ( $k$ ), use the formula $k = \frac{y}{x}$ . $\newline$ Calculation: $k = \frac{2 \text{ hours}}{5 \text{ pounds}} = 0.4 \text{ hours per pound}.$
Calculate Constant of Proportionality: Step $2$ : Write the equation representing the proportional relationship. $\newline$ Using the constant of proportionality, the equation for the relationship between the weight of the pot roast $x$ and the cooking time $y$ is $y = kx$ . $\newline$ Substitute $k = 0.4$ into the equation. $\newline$ Calculation: $y = 0.4x$ .

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