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Slope

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Source: — Data Sufficiency |
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by grockit_jake » Thu Oct 29, 2009 3:43 pm
Given that they intersect at a point (5,1) in this case, the other point is important in determining the slope.

If one line always hits the y-axis higher than the other, then that means

1. their slopes are different
2. If the slopes are positive, the slope of the line hitting highest on the y-axis (but below 1) is smaller than the slope of the other line
3. I the slope are negative, the slope of the line hitting lowest on the y-axis (but above 1) will be "larger" than the slope of the other line.

While the absolute values of the slopes switch, the line hitting higher on the y-axis will always have a lower slope, whether +/- or 0.
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by mridul_dave » Sun Nov 15, 2009 10:19 am
grockit_jake wrote:Given that they intersect at a point (5,1) in this case, the other point is important in determining the slope.

If one line always hits the y-axis higher than the other, then that means

1. their slopes are different
2. If the slopes are positive, the slope of the line hitting highest on the y-axis (but below 1) is smaller than the slope of the other line
3. I the slope are negative, the slope of the line hitting lowest on the y-axis (but above 1) will be "larger" than the slope of the other line.

While the absolute values of the slopes switch, the line hitting higher on the y-axis will always have a lower slope, whether +/- or 0.
Do we have to respond based on absolute values ?
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by Brent@GMATPrepNow » Sun Nov 15, 2009 10:58 am
mridul_dave wrote:
grockit_jake wrote:Given that they intersect at a point (5,1) in this case, the other point is important in determining the slope.

If one line always hits the y-axis higher than the other, then that means

1. their slopes are different
2. If the slopes are positive, the slope of the line hitting highest on the y-axis (but below 1) is smaller than the slope of the other line
3. I the slope are negative, the slope of the line hitting lowest on the y-axis (but above 1) will be "larger" than the slope of the other line.

While the absolute values of the slopes switch, the line hitting higher on the y-axis will always have a lower slope, whether +/- or 0.
Do we have to respond based on absolute values ?
You have some other options such as sketching and applying the slope formula.
Statement (1): lines pass through (5,1). We can sketch this to show that statement (1) is INSUFFICIENT
Image

Statement (2): the y-intercept of line n is greater than y intercept of line p.
We can use sketches to show that statement (2) is INSUFFIENT.
Image

Statements 1 and 2: Let n be the y-intercept of line n, and let p be the y-intercept of line p.
So, the two points of intersection with the y-axis are (0,n) and (0,p). We also know that n>p (from statement 2)

When we apply the slope formula, we get:
Slope of line n = (1-n)/(5-0)= (1-n)/5
Slope of line p = (1-p)/(5-0)= (1-p)/5
Since n>p, we know that (1-p)/5 (the slope of p) will be greater than (1-n)/5 (the slope of n)

So, statements 1&2 combined are SUFFICIENT
Answer = C
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by palvarez » Mon Nov 16, 2009 1:13 pm
okigbo wrote:Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p

Let n and p be slopes of n and p.

N: y = nx+a
P: y = px+b

1 = 5n +a = 5p +b
5(p-n) = a - b > 0

p - n > 0

C is the answer
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