At the deli counter in the supermarket, Nigel paid $10

Question

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)
y=

Answer 1

To create the equation for the proportional relationship between the weight of the deli meat and its cost, we start with the information given:

• Nigel paid $10 for 2.5 pounds of roast beef.

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

\[ y = kx \]

Where:

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

To find \( k \), we can use the information provided:

\[ y = 10 \quad \text{(the cost)} \] \[ x = 2.5 \quad \text{(the weight)} \]

Now, substituting these values into the equation:

\[ 10 = k(2.5) \]

To solve for \( k \), divide both sides by 2.5:

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

Now we can write the equation that represents the relationship:

\[ y = 4x \]

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

\[ y = 4x \]