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)

1 answer

To find the equation for the proportional relationship between the weight of deli meat and its cost, we can start by defining our variables:

  • Let \( x \) represent the weight of the roast beef in pounds.
  • Let \( y \) represent the cost of the roast beef in dollars.

Since the cost is proportional to the weight, we can express this relationship as:

\[ y = kx \]

where \( k \) is the constant of proportionality (the cost per pound of roast beef).

From the information given, Nigel paid $10 for 2.5 pounds of roast beef. We can plug these values into the equation to solve for \( k \):

\[ 10 = k(2.5) \]

To isolate \( k \), we divide both sides by 2.5:

\[ k = \frac{10}{2.5} = 4 \]

Now that we have the value of \( k \), we can write the equation of the line representing this proportional relationship:

\[ y = 4x \]

Thus, the equation for the graph of this proportional relationship is:

\[ y = 4x \]