<p>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 of l ???</p>
<p>I got 1 as the greatest possible value for the slope.
Here's how you do it:
x = y^2 - 4
for (0,p), 0 = p^2 -4, p = +/- 2
for (5,t), 5 = t^2 - 4, t = +/- 3
Now you have your points, it could be something like (0,2) (5,3), but you have to find the points combination that produces the greatest slope, either you see it right away that 3 - (-2) will produce 5 in the numerator for slope, and the denominator stays the same as 5 for all point combinations, then you would see that 5/5 = 1, that produces the greatest slope. If you didn't see that right away, you'd have to simple plug in the possible point values (using some common sense that automatically negative - negative won't get you anywhere, therefore you cut time) and you'd end up with 5/5 = 1. hope that helped =)</p>