An artist paints and sells square tiles. The selling price P , in dollars, of a painted tile is a

Question

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.

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

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

Accepted Answer

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 &ne;&#65024; 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.

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