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?

Answer 1

In a proportional relationship, one quantity is directly proportional to another, and the relationship can be expressed in the form of an equation:

\[ y = kx \]

where:

• \( y \) is the total cost,
• \( x \) is the weight of the deli meat (in pounds),
• \( k \) is the constant of proportionality (the price per pound).

Given that Nigel paid $10 for 212 pounds of roast beef, we can find the constant \( k \) by using the provided values:

\[ k = \frac{y}{x} = \frac{10}{212} \]

Calculating \( k \):

\[ k = \frac{10}{212} = \frac{5}{106} \]

Now, we can substitute \( k \) back into the proportional relationship equation:

\[ y = \frac{5}{106}x \]

Thus, the equation that represents the relationship between the cost \( y \) and the weight \( x \) of roast beef is:

\[ y = \frac{5}{106}x \]