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Question 1

A) At the deli counter in the supermarket, Nigel paid $10 for 21
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 = x

3 answers

To find the equation of the proportional relationship between the cost of the roast beef and its weight, we need to define what each variable represents:

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

From the problem, Nigel paid $10 for 2 pounds of roast beef. So we can find \( k \) using the given information:

\[ y = 10 \text{ dollars} \] \[ x = 2 \text{ pounds} \]

Substituting into the equation:

\[ 10 = k \cdot 2 \]

To find \( k \):

\[ k = \frac{10}{2} = 5 \]

Thus, the linear equation representing the relationship between the cost and the weight of the roast beef is:

\[ y = 5x \]

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

\[ y = 5x \]

Wrong.

I apologize for any confusion. Let's revisit the problem step-by-step to ensure we find the correct relationship.

Nigel paid $10 for 2 pounds of roast beef, so let's denote:

  • \( y \) as the cost in dollars,
  • \( x \) as the weight in pounds.

Given that cost is proportional to weight, we can express this relationship as:

\[ y = kx \]

To find the constant of proportionality \( k \), we can substitute the values we know:

\[ y = 10 \] (the cost) \[ x = 2 \] (the weight)

Now substituting these values into the equation:

\[ 10 = k \cdot 2 \]

Now solve for \( k \):

\[ k = \frac{10}{2} = 5 \]

This means the cost per pound of roast beef is $5.

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

\[ y = 5x \]

If you believe there was an error regarding the costs or weights, please clarify, and I'll rectify it. Thank you!