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:
\[ y = 4x \]