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Read the description of a proportional relationship. $\newline$ The Picture and Sound electronics store has hired Allie to work in the warehouse. She uses a pulley with a hand crank to lift heavy boxes. There is a proportional relationship between the number of times Allie turns the crank to lift a box, $x$ , and the height the box has been lifted (in feet), $y$ . $\newline$ She turns the crank $4$ times to lift a box $1$ foot. 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

The Picture and Sound electronics store has hired Allie to work in the warehouse. She uses a pulley with a hand crank to lift heavy boxes. There is a proportional relationship between the number of times Allie turns the crank to lift a box,

x

, and the height the box has been lifted (in feet),

y

.

\newline

She turns the crank

4

times to lift a box

1

foot. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Identify Given Values: Step $1$ : Identify the given values. $\newline$ Allie turns the crank $4$ times ( $x = 4$ ) to lift a box $1$ foot ( $y = 1$ ). $\newline$ Calculate the constant of proportionality, $k$ . $\newline$ $k = \frac{y}{x} = \frac{1}{4}$
Calculate Constant of Proportionality: Step $2$ : Write the equation using the constant of proportionality. $\newline$ The equation for the proportional relationship is $y = kx$ . $\newline$ Substitute $k = \frac{1}{4}$ into the equation. $\newline$ $y = \left(\frac{1}{4}\right)x$

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