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Algebra / Linear equations in two variables Difficulty: Medium

Side length, s (inches)	Price, P (dollars)
3	8.00
6	18.00
9	28.00

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.

Which of the following could define the relationship between s and P ?

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Explanation

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 = $the fraction 10 over 3$ . To solve for a, substitute one of the given pairs of values for s and P: when s = 3, P = 8, so $8 equals, the fraction 10 over 3, end fraction, times 3, plus a$ , which yields a = –2. The solution is therefore $P equals, the fraction 10 over 3, end fraction, times s minus 2$ .

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.