Graph Proportional Relationships Practice
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Question
At the deli counter in the supermarket, 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)
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Let's work through this problem step by step.
First, let's define the variables:
Let "C" represent the cost of deli meat in dollars.
Let "W" represent the weight of deli meat in pounds.
We know that the cost of deli meat is proportional to its weight. In this case, we are given that Nigel paid $10 for 212 pounds of roast beef. This means that when the weight of deli meat is 212 pounds, the cost is $10.
Let's use the general form for the equation of a proportional relationship: C = kW, where "k" represents the constant of proportionality.
We can plug in the values we know to find the value of "k":
10 = k * 212
Dividing both sides by 212, we get:
k = 10/212
Simplifying this fraction, we get:
k = 0.0472
So, the equation for the graph of this proportional relationship is:
C = 0.0472W
To find the equation for the graph of this proportional relationship, we need to determine the constant of proportionality, which represents the cost per pound of roast beef.
We can use the given information to set up a proportion:
$10/212 pounds = cost/x pounds
Simplifying the left side of the proportion, we get:
$0.0471698 = cost/x pounds
This shows that the cost per pound of roast beef is approximately $0.0471698. Therefore, the equation for the graph of this proportional relationship is:
cost = $0.0471698 * weight
To find the equation for the graph of this proportional relationship, we need to use the given information. We know that Nigel paid $10 for 212 pounds of roast beef.
Let's define the variables:
- Let x represent the weight of the roast beef in pounds.
- Let y represent the cost of the roast beef in dollars.
Based on the given information, we can set up a proportion: the cost of the roast beef is proportional to its weight.
$$\frac{y}{x} = \frac{10}{212}$$
To find the equation that represents this relationship, we need to isolate y. We can start by cross-multiplying:
$$212y = 10x$$
Next, we divide both sides of the equation by 212 to solve for y:
$$\frac{212y}{212} = \frac{10x}{212}$$
$$y = \frac{10}{212}x$$
Therefore, the equation for the graph of this proportional relationship is:
$$y = \frac{10}{212}x$$