PSAT Math Multiple-Choice Question 106: Answer and Explanation

Question: 106

The equation y = 3,100x + 105 models the relationship between the weight, y, in grams, of an average giant panda and the number of months, x, after it was born. If the equation is graphed in the xy-plane, what is indicated by the slope of the graph?

• A. The weight, in grams, of an average giant panda at birth
• B. The number of months it takes an average giant panda to gain weight
• C. The age, in months, of an average giant panda when it is fully matured
• D. The weight, in grams, that an average giant panda gains each month

Correct Answer: D

Explanation:

D

The question asks about the graph of the data representing a certain situation. Label the parts of the equation to determine what they represent. In this question, y represents the weight of the giant panda and x represents the number of months after the panda was born. The slope of a graph is defined as the change in y over the change in x, so the slope must relate to weight, not time. Eliminate (B) and (C) for this reason. The equation is in y = mx + b form, where m is the slope of a graph, so here the slope is 3,100. Plug and play to determine what gives a value of 3,100. Make m = 0 to get the giant panda's weight after 0 months, or at birth. This becomes weight = 3,100(0) + 105 or weight = 105. Since the giant panda's weight at birth is not 3,100, eliminate (A). After one month, the giant panda will have a weight = 3,100(1) + 105 = 3,100 + 105 = 3,205. Therefore, in the first month, the panda gained 3,205 - 105 = 3,100 grams in weight. The correct answer is (D).