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Read the description of a proportional relationship. $\newline$ When a truck full of boxes arrives at the Weston Post Office, Bill unloads the truck by placing the boxes on a conveyor belt. Bill's coworkers are impressed with how fast Bill does his job. There is a proportional relationship between the time (in minutes) Bill spends unloading the truck, $x$ , and the number of boxes he unloads from the truck, $y$ . $\newline$ In $1$ minute, Bill unloads $6$ boxes from the truck. 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

When a truck full of boxes arrives at the Weston Post Office, Bill unloads the truck by placing the boxes on a conveyor belt. Bill's coworkers are impressed with how fast Bill does his job. There is a proportional relationship between the time (in minutes) Bill spends unloading the truck,

x

, and the number of boxes he unloads from the truck,

y

.

\newline

In

1

minute, Bill unloads

6

boxes from the truck. 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. $\newline$ We know: $\newline$ Time, $x = 1$ minute $\newline$ Number of boxes, $y = 6$ boxes
Calculate Constant of Proportionality: Step $2$ : Calculate the constant of proportionality, $k$ . Constant of proportionality, $k = \frac{y}{x}$ $k = \frac{6}{1}$ $k = 6$
Write Proportional Relationship Equation: Step $3$ : Write the equation for the proportional relationship using the constant of proportionality. $\newline$ Equation for proportional relationship: $y = kx$ $\newline$ $y = 6x$

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