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Read the description of a proportional relationship.\newlineEvery 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, xx, and the weight (in pounds) of the peas he has shelled, yy.\newlineAfter 66 minutes, Kenny has shelled 33 pounds of peas. Write the equation for the relationship between xx and yy.\newliney=__y = \_\_

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Q. Read the description of a proportional relationship.\newlineEvery 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, xx, and the weight (in pounds) of the peas he has shelled, yy.\newlineAfter 66 minutes, Kenny has shelled 33 pounds of peas. Write the equation for the relationship between xx and yy.\newliney=__y = \_\_
  1. 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 33 pounds in 66 minutes. So, the constant of proportionality (kk) is calculated by dividing the weight by the time: k=3 pounds6 minutes=0.5 pounds per minute.k = \frac{3 \text{ pounds}}{6 \text{ minutes}} = 0.5 \text{ pounds per minute}.
  2. 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=kxy = kx, where yy is the total weight of the peas shelled, xx is the time spent shelling peas, and kk is the constant of proportionality. Substituting the value of kk we found, the equation becomes y=0.5xy = 0.5x.

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