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Maximum number of Number of cars passengers and crew 3 174 5 284 10 559 The table shows the linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p, that the train can carry. Which equation represents the linear relationship between c and p? 55c−p = −9
Correct answer: A (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice A is correct. It’s given that there is a linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p, that the train can carry. It follows that this relationship can be = + represented by an equation of the form p mc b, where m is the rate of change of p in this relationship and b is a constant. The rate of change of p in this relationship can be calculated by dividing the difference in any two values of p by the difference in the corresponding values of c. Using two pairs of values given in 284-174 the table, the rate of change of p in this relationship is 5-3 , or 55. = + = + Substituting 55 for m in the equation p mc b yields p 55c b. The value of b can be found by substituting any value of c and its corresponding value of p 10 559 for c and p, respectively, in this equation. Substituting for c and for p 559=55 10+ 559=550+ 550 yields ^ h b, or b. Subtracting from both sides of this = = + equation yields 9 b. Substituting 9 for b in the equation p 55c b yields =55 +9 -9=55 p c . Subtracting 9 from both sides of this equation yields p c. -9=55 - Subtracting p from both sides of this equation yields c p, or 55 - =-9 c p . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
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