To find the equation for the proportional relationship between the cost of deli meat and its weight, we can use the formula for direct variation, which is:
\[ y = kx \]
where:
- \( y \) is the total cost,
- \( x \) is the weight of the meat in pounds,
- \( k \) is the constant of proportionality (the cost per pound).
From the information given, Nigel paid $10 for 2.5 pounds of roast beef. We can determine \( k \) as follows:
- Use the values \( y = 10 \) and \( x = 2.5 \):
\[ 10 = k \times 2.5 \]
- To find \( k \), divide both sides by 2.5:
\[ k = \frac{10}{2.5} = 4 \]
So the constant of proportionality \( k \) is $4 per pound.
Now we can write the equation for the cost \( y \) in terms of the weight \( x \):
\[ y = 4x \]
This is the equation for the graph of the proportional relationship between the cost of deli meat and its weight.