At the deli counter in the supermarket, Nigel paid $10 for 2 1/2 pounds of roast beef that cost of deli meat is proportional to its weight. What is the equation for the graph of this proportional relationship?
Let x be the weight (in pounds) of the roast beef and y be the cost of the deli meat.
According to the given information, we know that when x = 2.5, y = 10.
The equation for a proportional relationship is of the form y = mx, where m is the constant of proportionality.
To find the value of m, we can use the given data:
m = y / x = 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 need to determine the constant of proportionality. In this case, the cost of deli meat is proportional to its weight.
Let's denote the weight of the deli meat as x (in pounds) and the cost as y (in dollars). We know that Nigel paid $10 for 2 1/2 pounds of roast beef.
First, let's convert 2 1/2 pounds into a decimal form. Since 1/2 is equivalent to 0.5, we have 2.5 pounds.
Now, we can set up a proportion to find the constant of proportionality. The equation for a proportional relationship is y = kx, where k is the constant of proportionality.
Here is the proportion based on the given information:
10 / 2.5 = k / x
To find the value of k, we'll solve for k in the equation. Cross-multiplying, we have:
10x = 2.5k
To isolate k, divide both sides of the equation by 2.5:
k = 10x / 2.5
Simplifying further, we get:
k = 4x
Therefore, the equation for the graph of this proportional relationship is:
y = 4x