At a deli counter in the supermarket, Nigel paid $10 for 2 1/2 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?
To find the equation for the graph of this proportional relationship, we need to determine the constant of proportionality.
We know that Nigel paid $10 for 2 1/2 pounds of roast beef. We can set up a proportion using this information:
10 dollars / 2.5 pounds = x dollars / 1 pound
To find the value of x, we can cross-multiply:
10 * 1 = 2.5 * x
10 = 2.5x
Now, we can solve for x by dividing both sides of the equation by 2.5:
10 / 2.5 = x
4 = x
Therefore, the constant of proportionality is 4. This means that for every pound of roast beef, Nigel pays $4.
Now we can write the equation for the graph of this proportional relationship:
y = 4x
Where y represents the cost in dollars and x represents the weight in pounds.
Let's assume that the cost of deli meat is denoted by C and the weight of the deli meat is denoted by W.
We know that the cost of deli meat is proportional to its weight, so we can write this as:
C = kW
Where k is the proportionality constant.
From the information given, we know that Nigel paid $10 for 2 1/2 pounds of roast beef. This means that when W = 2 1/2, C = 10.
Plugging these values into the equation, we get:
10 = k(2 1/2)
To simplify this equation, we convert 2 1/2 to a mixed number or improper fraction:
2 1/2 = 5/2
10 = k(5/2)
To isolate k, we divide both sides of the equation by 5/2:
10 / (5/2) = k
Simplifying the right side of the equation, we get:
10 * (2/5) = k
4 = k
Therefore, the equation for the graph of this proportional relationship is:
C = 4W
To find the equation for the graph of this proportional relationship, we can use the formula for a proportional relationship which states that y = kx, where y represents the cost of the deli meat, x represents the weight of the deli meat, and k represents the constant of proportionality.
In this case, we know that Nigel paid $10 for 2 1/2 pounds of roast beef. We can convert 2 1/2 pounds to 2.5 pounds. So, we have:
y = kx
10 = k(2.5)
We can solve for k by dividing both sides of the equation by 2.5:
10/2.5 = k(2.5)/2.5
4 = k
Therefore, the equation for the graph of this proportional relationship is y = 4x.