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Linear equations in two variables SAT question
Math · Algebra · Medium · Answer it here, explanation included.
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 ?
ExplanationShow
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.
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