Bunuel wrote:
If the graph of the function x=y^2–9 on the xy-coordinate plane intersects line l at points A and B, what is the greatest possible slope of line l?
(1) Point A has coordinates (0,a)
(2) Point B has coordinates (7,b)
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:Correct answer: (C)
Solution: We will have sufficient information if we can account for all possible variations in line 1. To determine the slope, we need two sets of coordinate points. Slope is defined by the following formula: \(\frac{(y_2−y_1)}{(x_2−x_1)}\)
Each statement by itself is insufficient. Statement (1) tells us about the coordinates of Point A, but nothing about the coordinates of Point B. And Statement (2) tells us about the coordinates of Point B, but nothing about the coordinates of Point A. However, when the two statements are combined, we can determine the greatest possible slope of line l.
Where two lines intersect, their coordinates are identical, and their equations are equal to each other. So each of the two points given in Statements 1 and 2 must satisfy the function x=y^2–9. Plugging the coordinate values of Point A into the equation, we get 0=a^2–9. Solving for a, we get that a is equal to 3 or -3. Thus, the possible coordinates of Point A are (0, 3) and (0,-3). Plugging the coordinates of Point B into the equation, we get 7=b^2–9. Solving for b, we get that b is equal to 4 or -4. Thus, the possible coordinates of Point B are (7, 4) and (7, -4).
Given these coordinate options for points A and B, there are four possible forms line 1 could take. With this information, we can determine which of the four possible slopes yields the greatest value. However, there is no need to actually calculate which line has the greatest slope.
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