SOLUTION: In the xy-coordinate plane, the graph of x = y^2 - 4 intersects line L at (0,p) and (5,t). What is the greatest possible value of the slope L?

Question 366455: In the xy-coordinate plane, the graph of x = y^2 - 4 intersects line L at (0,p) and (5,t). What is the greatest possible value of the slope L?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
First of all the graph of the relation is a parabola lying sideways opening to the right , having y-intercepts (0,2) and (0,-2), and vertex (-4,0). Since L intersects the parabola at (0,p), p is either 2 or -2. Also, since (5,t) is an intersection point, t is either 3 or -3. (Why?)Hence there are four possible lines:
1) One passing through (0,2) and (5,-3) with slope -1,
2) One passing through (0,-2) and (5,-3) with slope -1/5,
3)One passing through (0,2) and (5,3) with slope 1/5,
4)One passing through (0,-2) and (5,3) with slope 1.
So now you know the answer! =)
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