Number of cars Maximum number of passengers and crew 3 174 5 284 10 559 The table shows the linear

Question

Number of cars	Maximum number of 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 $p$ ?

A.

$55 c - p = - 9$

B.

$55 c - p = 9$

C.

$55 p - c = - 9$

D.

$55 p - c = 9$

Accepted Answer

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 = m c + 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 the table, the rate of change of p in this relationship is 284 - 174 5 - 3 , or 55 . Substituting 55 for m in the equation p = m c + b yields p = 55 c + b . The value of b can be found by substituting any value of c and its corresponding value of p for c and p , respectively, in this equation. Substituting 10 for c and 559 for p yields 559 = 55 10 + b , or 559 = 550 + b . Subtracting 550 from both sides of this equation yields 9 = b . Substituting 9 for b in the equation p = 55 c + b yields p = 55 c + 9 . Subtracting 9 from both sides of this equation yields p - 9 = 55 c . Subtracting p from both sides of this equation yields - 9 = 55 c - p , or 55 c - p = - 9 . 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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