Statement 1: Lines n and p intersect at point (5,1).

With only one point with which to work and no other information, we cannot determine anything about the slopes of the lines.

Insufficient.

Statement 2: The y intercept of line n is greater than the y intercept of line p.

The lines could have various different slopes irrespective of the relative values of their y intercepts.

Insufficient.

Statements Combined:

From Statement 1 we know that the lines intersect in a particular spot, (5, 1), above the x axis and to the right of the y axis.

From Statement 2 we know that when x = 0, the y value of line n is greater than the y value of line p.

No matter what those y intercepts are, the change in y for n when x goes from 0 to 5 will be less than the change in y for p when x goes from 0 to 5, because n is starting from a higher y when x = 0, and both n and p go to y = 1 when x = 5.

For example if the y intercepts of n and p are 2 and 1 respectively, when x increases from 0 to 5, the change in the y of n will be -1 and the change in the y of p will be 0. So n would have a negative slope and p would have a slope of 0.

Since for a given positive change in x the change in y is less for n than for p, the slope of n is less than the slope of p.

Sufficient.

The correct answer is C.

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5,1).
(2) The y-intercept of line n is greater than the y-intercept of line p.

Statement 1: Lines n and p intersect at the point (5,1).
No way to determine whether the slope of line n is less than the slope of line p.
INSUFFICIENT.

Statement 2: The y-intercept of line n is greater than the y-intercept of line p.
No way to determine whether the slope of line n is less than the slope of line p.
INSUFFICIENT.

Statements 1 and 2 combined:
Case 1: y-intercept of n is (0,2), line intercept of p is (0,1)
Since (5,1) is on each line, we get:
Slope of n = (1-2)/(5-0) = -1/5.
Slope of p = (1-1)/(5-0) = 0.
The slope of n is less than the slope of p.

Case 2: y-intercept of n is (0,10), line intercept of p is (0,-1)
Since (5,1) is on each line, we get:
Slope of n = (1-10)/(5-0) = -9/5.
Slope of p = (1- (-1))/(5-0) = 2/5.
The slope of n is less than the slope of p.

Case 3: y-intercept of n is (0,-1), line intercept of p is (0,-10)
Since (5,1) is on each line, we get:
Slope of n = (1-(-1))/(5-0) = 2/5
Slope of p = (1- (-10))/(5-0) = 11/5.
The slope of n is less than the slope of p.

In every case, the slope of n is less than the slope of p.
SUFFICIENT.

The correct answer is C.