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?

Answer 1

Let x represent the weight of roast beef in pounds and y represent the cost of the roast beef in dollars.

Since the cost of deli meat is proportional to its weight, we can write the equation for the proportionality as:

y = kx

where k is the constant of proportionality.

We are given that Nigel paid $10 for 2 1/2 pounds of roast beef, so we can substitute these values into the equation to find the value of k.

10 = k * 2 1/2

In order to simplify the equation, we can convert 2 1/2 to an improper fraction:

10 = k * 5/2

To find the value of k, we divide both sides of the equation by 5/2:

10 / (5/2) = k

To divide by a fraction, we multiply by its reciprocal:

10 * (2/5) = k

Simplifying this expression, we get:

k = 4

Therefore, the equation for the graph of the proportional relationship between weight and cost is:

y = 4x