Darla has a recipe for pot roast. There is a proportional relationship between the weight (in pounds) of the pot roast, x, and the total cooking time (in hours), y. Her recipe says that a 6-pound pot roast should take 3 hours to cook.
The equation for the relationship between x and y is Response area = Response areaResponse area
If Darla's pot roast weighs Response area pounds, it will take Response area hours to cook.
The equation for the relationship between x and y is y = (3/6)x.
If Darla's pot roast weighs x pounds, it will take y hours to cook.
The equation for the proportional relationship between the weight (x) of the pot roast and the cooking time (y) is:
y = (3/6) * x
If Darla's pot roast weighs "a" pounds, it will take "b" hours to cook. Plugging the values into the equation, we get:
b = (3/6) * a
So, if Darla's pot roast weighs "a" pounds, it will take "b" hours to cook.
To find the equation for the relationship between the weight of the pot roast, x, and the total cooking time, y, we can use the given information that a 6-pound pot roast takes 3 hours to cook.
Step 1: Identify the proportional relationship:
Since there is a proportional relationship, we can assume that the weight and cooking time have a direct proportion. This means that as the weight increases, the cooking time also increases in a consistent manner.
Step 2: Determine the constant of proportionality:
To find the constant of proportionality, we can use the values from the given information. We know that when x = 6 pounds, y = 3 hours. Thus, the constant of proportionality is 3/6 = 1/2.
Step 3: Write the equation for the relationship:
The equation for a proportional relationship can be written in the form y = kx, where k is the constant of proportionality. In this case, the equation becomes y = (1/2)x.
Step 4: Use the equation to solve the problem:
To find the total cooking time for a pot roast weighing a specific number of pounds, substitute that value into the equation. Let's say the pot roast weighs x pounds, then the total cooking time would be y = (1/2)x hours.
So, if Darla's pot roast weighs x pounds, it will take (1/2)x hours to cook.
The final equation for the relationship between the weight and cooking time is:
y = (1/2)x.