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14 years ago

This is a sample SAT question. I have worked out the answer to be 1/5 but the book says the answer is 1. Any explanation?

Top 4 Answers

14 years ago

So the graph in question is
x = y^2 - 4
and it intersects line L at (0,p) and (5,t)
m = (t - p) / (5 - 0) = (1/5)(t - p)
We know that the points (0,p) and (5,t) are part of the graph
x = y^2 - 4. Thus,
If x = 0, y = p:
0 = p^2 - 4
0 = (p - 2)(p + 2), implying p = {-2, 2}
If x = 5, y = t:
5 = t^2 - 4
0 = t^2 - 9 = (t - 3) (t + 3), implying t = {3, -3}
Since m = (1/5) (t - p), all we have to do is plug in every possibility for t and p and find out what the greatest value is.
p = -2, t = -3
m = (1/5) (-3 - (-2)) = (1/5) (-3 + 2) = (1/5)(-1) = -1/5
p = -2, t = 3
m = (1/5) (3 - (-2)) = (1/5) (3 + 2) = 5/5 = 1
p = 2, t = -3
m = (1/5) (-3 - 2)) = (1/5) (-5) = -1
p = 2, t = 3
m = (1/5) (3 - 2) = (1/5)(1) = 1/5
That means we get the maximum of {-1/5, 1, -1, 1/5}, which is 1.
The greatest possible slope occurs when p = -2, t = 3, and the slope is equal to 1.

0

14 years ago

The graph is a parabola open to the left.
At x = 0, p = Â±2; at x = 5, t = Â±3.
The slope of the line is defined as (t-p)/(5-0).
Therefore the maximum slope is obtained when you pick t = 3 and p = -2.
The maximum slope = (3--2)/5 = 1

0

14 years ago

I assume you got p=2 and t=3, right?
remember that p and t can be negative, too! if you use the points (0,-2) and (5,3), then the answer is 1.

0

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