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Read the description of a proportional relationship. $\newline$ Every few years, Russell's entire family gets together for a family reunion. This year, Russell's parents are hosting, and they have to cook a lot of food to feed the crowd. Russell has volunteered to do the most tedious job: shelling peas. There is a proportional relationship between the amount of time (in minutes) Russell spends shelling peas, $x$ , and the weight (in pounds) of the peas he has shelled, $y$ . $\newline$ After $10$ minutes, Russell has shelled $2$ 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, Russell's entire family gets together for a family reunion. This year, Russell's parents are hosting, and they have to cook a lot of food to feed the crowd. Russell has volunteered to do the most tedious job: shelling peas. There is a proportional relationship between the amount of time (in minutes) Russell spends shelling peas,

x

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

y

.

\newline

After

10

minutes, Russell has shelled

2

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, $k$ , which is the ratio of $y$ (pounds of peas) to $x$ (minutes spent shelling). We use the given values: $x = 10$ minutes and $y = 2$ pounds. Calculate $k$ by dividing $y$ by $x$ .
Write Proportional Relationship Equation: Next, we write the equation of the proportional relationship using the constant of proportionality, $k$ . The general form of the equation for a proportional relationship is $y = kx$ . Substitute $k = 0.2$ into the equation.

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