To express the relationship between the weight of the roast beef and its cost, we can use the formula for direct variation, which is:
\[ y = kx \]
where:
- \( y \) is the total cost,
- \( x \) is the weight in pounds,
- \( k \) is the constant of proportionality (cost per pound).
From the information given:
- Nigel paid $10 for 2.5 pounds of roast beef. So we can substitute these values into the equation to find \( k \):
\[ 10 = k \cdot 2.5 \]
To find \( k \), we can solve for it:
\[ k = \frac{10}{2.5} \]
Calculating that gives:
\[ k = 4 \]
Now we have the value of \( k \), we can write the equation:
\[ y = 4x \]
This means that the cost \( y \) in dollars is equal to 4 times the weight \( x \) in pounds of the roast beef. Thus, the equation for the graph of this proportional relationship is:
\[ y = 4x \]