At the 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? (1 point)
Let x be the weight of the roast beef in pounds and y be the cost of the roast beef.
We are given that Nigel paid $10 for 2 1/2 pounds of roast beef. Therefore, the cost per pound of roast beef is $10/(2 1/2) = $10/(5/2) = $10 * (2/5) = $4.
Therefore, the equation for the graph of this proportional relationship is y = 4x
To find the equation for the graph of this proportional relationship, we can use the formula for direct proportionality: y = kx, where y is the cost of deli meat, x is the weight of deli meat, and k is the constant of proportionality.
In this case, Nigel paid $10 for 2 1/2 pounds of roast beef, so we can set up the equation as follows:
10 = k * 2.5
To solve for k, divide both sides of the equation by 2.5:
10 / 2.5 = k
4 = k
Therefore, the equation for the graph of this proportional relationship is y = 4x.
To find the equation for the graph of the proportional relationship, we need to determine the constant of proportionality. In this case, the constant of proportionality represents the cost per pound of roast beef.
We are given that Nigel paid $10 for 2 1/2 pounds of roast beef. To find the cost per pound, we divide the total cost by the weight:
Cost per pound = Total cost / Weight
Total cost = $10
Weight = 2 1/2 pounds = 5/2 pounds
Substituting the values into the equation, we get:
Cost per pound = $10 / (5/2) pounds
Simplifying further:
Cost per pound = $10 * (2/5) pounds
Cost per pound = $4 per pound
Therefore, the cost per pound of roast beef is $4.
Now we can write the equation for the graph of this proportional relationship. Let "x" represent the weight of the roast beef (in pounds) and "y" represent the cost of the roast beef (in dollars).
The equation is:
y = 4x
This equation shows that the cost (y) is equal to the weight (x) multiplied by the constant of proportionality (4), which represents the cost per pound of roast beef.