Section C Section C Checkpoint

Problem 1

A fashion designer orders leather by the square meter. The table shows their last four orders. They are wondering if they get a better deal when they place a larger order.

Do the values in the table show evidence of a proportional relationship? Explain or show your reasoning.

square meters of leather	price in dollars
40	740.00
20	370.00
35	647.50
52	962.00

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Solution

Yes. Dividing the price by the square meters of leather gets 18.5 for each row.

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Sample Response

Yes. Dividing the price by the square meters of leather gets 18.5 for each row.

Problem 2

The equation $y = 16 \div x$ represents the relationship between the length, $x$ , and width, $y$ , of a rectangle whose area is 16 square units.

Complete the $y$ column of the table with values that make the equation $y = 16 \div x$ true.
Is there a proportional relationship between $x$ and $y$ ? Explain how you know. (It may help to complete the $\frac{y}{x}$ column.)

$x$	$y$	$\frac{y}{x}$
1
2
4
8

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Solution

16, 8, 4, 2
No. Sample reasoning: $\frac{y}{x}$ is not the same for every pair of values that make the equation true.

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Sample Response

16, 8, 4, 2
No. Sample reasoning: $\frac{y}{x}$ is not the same for every pair of values that make the equation true.