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)

## Data Sufficiency- 700 level

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- kinshuk97gupta
- Junior | Next Rank: 30 Posts
**Posts:**10**Joined:**28 Jan 2019

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.