At the deli counter in the supermarket, Nigel paid $10 for 212 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)
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To find the equation for the graph of this proportional relationship, we can use the formula for a proportional relationship, which is:
\(y = kx\)
where \(y\) represents the cost of the deli meat, \(x\) represents the weight of the deli meat, and \(k\) represents the proportionality constant.
In this case, we know that Nigel paid $10 for 212 pounds of roast beef. So we can substitute these values into the formula to solve for \(k\):
\(10 = k \times 212\)
To find the value of \(k\), we can divide both sides of the equation by 212:
\(\frac{10}{212} = k\)
Simplifying the right side of the equation gives us:
\(k = \frac{5}{106}\)
Now we can substitute this value of \(k\) back into the equation to get the final equation for the graph of this proportional relationship:
\(y = \frac{5}{106}x\)
Let $C$ be the cost and $w$ be the weight of the deli meat. The cost is proportional to the weight, which can be represented by the equation $C = k \cdot w$, where $k$ is a constant.
To find the value of $k$, we can use the given information that Nigel paid $10 for 212 pounds of roast beef. Plugging these values into the equation, we have $10 = k \cdot 212$.
Simplifying the equation, we divide both sides by 212 to solve for $k$:
$$
\begin{aligned} 10 &= k \cdot 212 \\ \frac{10}{212} &= k \end{aligned}
$$
So we have $k = \frac{10}{212}$.
Therefore, the equation for the graph of this proportional relationship is:
$$
C = \frac{10}{212} \cdot w
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To find the equation for the graph of this proportional relationship, we need to determine the constant of proportionality.
In this case, the amount paid, $10, is proportional to the weight of the roast beef, 212 pounds.
To find the constant of proportionality, we divide the amount paid by the weight of the roast beef:
constant of proportionality = amount paid / weight of roast beef
constant of proportionality = $10 / 212 pounds
Simplifying the fraction, we get:
constant of proportionality ≈ $0.0472 per pound
Now that we have the constant of proportionality, we can write the equation for the graph of this proportional relationship:
amount paid = constant of proportionality × weight of roast beef
amount paid = $0.0472 per pound × weight of roast beef
Therefore, the equation for the graph of this proportional relationship is:
amount paid = 0.0472w
Where w represents the weight of the roast beef.