An artist paints and sells square tiles. The selling price P, in dollars, of a painted tile is a linear function of the side length of the tile s, in inches, as shown in the table below.
\n| Side length, s (inches) | \nPrice, P (dollars) | \n
| 3 | \n8.00 | \n
| 6 | \n18.00 | \n
| 9 | \n28.00 | \n
Which of the following could define the relationship between s and P ?
\n","rationale_html":"Choice C is correct. The relationship between s and P can be modeled by a linear equation of the form P = ks + a, where k and a are constants. The table shows that P increases by 10 when s increases by 3, so k = . To solve for a, substitute one of the given pairs of values for s and P: when s = 3, P = 8, so
, which yields a = –2. The solution is therefore
.
Choice A is incorrect. When s = 3, P = 8, but 3(3) + 10 = 19 ≠︀ 8. Choice B is incorrect. This may result from using the first number given for P in the table as the constant term a in the linear equation P = ks + a, which is true only when s = 0. Choice D is incorrect and may result from using the reciprocal of the slope of the line.
\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.634000+00:00","source_updated_at":"2023-08-02T20:25:59.634000+00:00","options":[{"label":"A","content_html":"\n \n \n
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