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?

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 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 = 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 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 = 55c + b yields p = 55c + 9. Subtracting 9 from both sides of this equation yields p - 9 = 55c. Subtracting p from both sides of this equation yields -9 = 55c - p, or 55c - p = -9.