Nigel paid $10 for 212 pounds of roast beef. The cost of deli meat is proportional to its weight. What is the equation for the graph of this proportional relationship?(1 point)
The equation for the graph of this proportional relationship can be written as:
Cost = (Cost per pound) * (Weight),
where "Cost" represents the cost of the deli meat in dollars, "Cost per pound" represents the cost of the meat per pound, and "Weight" represents the weight of the deli meat in pounds.
In this case, since Nigel paid $10 for 212 pounds of roast beef, the Cost per pound would be:
Cost per pound = $10 ÷ 212 = $0.047169811...
(approximately $0.047)
Therefore, the equation for the graph of this proportional relationship can be written as:
Cost = $0.047 * Weight.
To find the equation for the graph of this proportional relationship, we need to determine the constant of proportionality.
Let the cost of deli meat be represented by C, and the weight of the meat be represented by W.
We know that Nigel paid $10 for 212 pounds of roast beef. This gives us the following data point: (W, C) = (212, 10).
Since the cost of deli meat is proportional to its weight, we can write the equation as:
C = k * W,
where k represents the constant of proportionality.
To find the value of k, we can use the given data point.
10 = k * 212.
Dividing both sides of this equation by 212 gives:
k = 10/212.
So, the equation for the graph of this proportional relationship is:
C = (10/212) * W.
To find the equation for the graph of this proportional relationship, we need to determine the constant of proportionality. In this case, the cost of deli meat is proportional to its weight.
We can set up a proportion to find the constant of proportionality:
Cost/Weight = Constant
Let's use the given information to set up the proportion:
$10 / 212 pounds = Constant
To solve for the constant, we can divide $10 by 212:
Constant = $10 / 212 ≈ 0.0471698113
Therefore, the constant of proportionality is approximately 0.0471698113.
Now we can write the equation for the graph of this proportional relationship:
Cost = Constant * Weight
Using the constant we found, the equation is:
Cost = 0.0471698113 * Weight