Question

At the deli counter in the supermarket, Nigel paid \$ 10for * 2 1/9 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 = Box x

Answer 1

Let x represent the weight of the roast beef in pounds.
The proportionality constant, or constant of variation, can be found by dividing the total cost by the weight:
constant of variation = cost/weight = (10)/(2 \(\frac{1}{9}\))
To convert the mixed number to an improper fraction, we have:
2 \(\frac{1}{9}\) = \(\frac{18}{9}\) + \(\frac{1}{9}\) = \(\frac{19}{9}\)
Dividing 10 by \(\frac{19}{9}\) gives us:
constant of variation = 10 ÷ \(\frac{19}{9}\)
To divide by a fraction, we can multiply by its reciprocal:
constant of variation = 10 x \(\frac{9}{19}\)
constant of variation = \(\frac{90}{19}\)
So, the equation for the graph of this proportional relationship is:
y = \(\frac{90}{19}\)x