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.
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 concept of proportionality.
We are given that when the pot roast weighs 6 pounds, it takes 3 hours to cook. This gives us one point on the graph. Let's call it (x1, y1), where x1 = 6 pounds and y1 = 3 hours.
Now, let's find the equation for this proportional relationship.
The general equation for a proportional relationship is y = kx, where k is the constant of proportionality. In our case, y represents the cooking time (in hours) and x represents the weight of the pot roast (in pounds).
To find the constant of proportionality, we can use the given data point (x1, y1) which is (6, 3). We substitute these values into the equation:
3 = k * 6
To isolate k, we divide both sides of the equation by 6:
3/6 = k
k = 1/2
Now, we can substitute the value of k back into the general equation:
y = (1/2)x
Therefore, the equation for the relationship between the weight of the pot roast, x, and the total cooking time, y, is: y = (1/2)x.
Using this equation, we can find the cooking time for any given weight of the pot roast. If the pot roast weighs x pounds, it will take (1/2)x hours to cook.