Data Sufficiency

Can someone explain? Thanks!

IS it C?

Is slope of line n < slope of line p?

(1) the point of intersection tells us nothing about the respective slopes: insufficient.

(2) the y intercepts tell us nothing about the respective slopes: insufficient.

Together:

from (1), we know that the lines intersect in quadrant 1 (+,+).

From (2), we know that line n crosses the y-axis higher than does line p.

For a line that has points in quadrant 1, the LOWER the y-intercept, the HIGHER the slope will be. Let's examine the 3 possible cases:

(1) y-intercept = 1

This line will be parallel to the x-axis and have a slope of 0.

(2) y-intercept > 1

This line will slope from upper right to bottom left and have a negative slope. The higher we start, the MORE negative the slope will be.

(3) y-intercept < 1

This line will slope from lower left to upper right and have a positive slope. The lower we start, the MORE positive the slope will be.

So, if n has a bigger y-int than does p, line n will definitely have a smaller slope: sufficient, choose (C).

hi stuart,
please let me know if this can be used

general equation of st line

ax+by+c =0

x intercept = -c/a => a = -c/x-intercept

y intercept = -c/b ==> b = -c/y intercept

slope = -a/b ==> k/x-intercept/k/y-intercept

so as the lines have point in quad 1. the value of y intercept is inversely proportional to slope.
Hence C.

Is this approach right?
Please help.

if

now to compare slopes of two lines

IMO C

Equation : y=mx+c

From 1 ,

N-----y1= m1x1+c1

Therefore, 1 = 5m1+c1

Similarly, L---- 1=5m2+c2

From 2, c1>c2


subtracting equation in 1

5(m1-m2) + c1-c2) = 0

5(m1-m2) = - (c1-c2) = c2-c1

But c1>c2

Therefore, 5(m1-m2) <0
i.e m1<m2

ANs C