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Read the description of a proportional relationship. $\newline$ Every few years, Kenny's entire family gets together for a family reunion. This year, Kenny's parents are hosting, and they have to cook a lot of food to feed the crowd. Kenny has volunteered to do the most tedious job: shelling peas. There is a proportional relationship between the amount of time (in minutes) Kenny spends shelling peas, $x$ , and the weight (in pounds) of the peas he has shelled, $y$ . $\newline$ After $6$ minutes, Kenny has shelled $3$ pounds of peas. 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

Every few years, Kenny's entire family gets together for a family reunion. This year, Kenny's parents are hosting, and they have to cook a lot of food to feed the crowd. Kenny has volunteered to do the most tedious job: shelling peas. There is a proportional relationship between the amount of time (in minutes) Kenny spends shelling peas,

x

, and the weight (in pounds) of the peas he has shelled,

y

.

\newline

After

6

minutes, Kenny has shelled

3

pounds of peas. Write the equation for the relationship between

x

and

y

.

\newline

y = \_\_

Find Constant of Proportionality: First, we need to find the constant of proportionality, which is the ratio of the weight of the peas shelled to the time spent shelling them. We know that Kenny shelled $3$ pounds in $6$ minutes. So, the constant of proportionality ( $k$ ) is calculated by dividing the weight by the time: $k = \frac{3 \text{ pounds}}{6 \text{ minutes}} = 0.5 \text{ pounds per minute}.$
Write Proportional Relationship Equation: Now, we can write the equation of the proportional relationship using the constant of proportionality. The general form of the equation for a proportional relationship is $y = kx$ , where $y$ is the total weight of the peas shelled, $x$ is the time spent shelling peas, and $k$ is the constant of proportionality. Substituting the value of $k$ we found, the equation becomes $y = 0.5x$ .

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