Slope

[okigbo]

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

[grockit_jake]

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.

[mridul_dave]

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 ?

[Brent@GMATPrepNow]

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


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.


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

[palvarez]

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