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Lines n and p lie in the xy-plane. Is the slope of line n [#permalink]
11 Nov 2006, 12:28

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.

I keep ending up with answer E - both statements together are not sufficient. However, this is not the correct answer.

Here's my work, using the equation for a line, y = Mx + B, where M is slope and B is y-intercept.

(1) 5 * Mn + Bn = 5 * Mp + Bp
Not sufficient

(2) Obviously not sufficient

(1 & 2 together) 5 * Mn + Bn = 5 * Mp + Bp
Simplifying this equation gives:
Mp / Mn = Bn - Bp

So, to know if slope of line n is less than slope of line p, we have to know whether the left hand side of this equation is greater than 1. For it to be greater than 1, Bn has to be at least 1 greater than Bp, but we don't know that for sure. We only know that Bn is greater than Bp, not to what extent.

I don't get the algebraic method.. however I was thinking that if the points intersect, then the line originating higher, or sufficiently lower than the other would result in a greater slope (assuming the slope can be positive or negative). But, if the y intercept for n is +1 and the y intercept for point P is -5, isnt the slope greater for P?

At first it was straight C, until I drew a picture on my scrap paper and realized that a higher Y intercept doesn't seem to necessarily mean a greater slope.

I am going wrong somewhere!! Help!

Here is the algebraic method
each statement is individually insuff.
Combining we get
Let the eq of two lines be y1=m1x1+c1 and y2=m2x2+c2
Now the pt (5,1) lies on both lines so must satisfy the above equations
1=5m1+c1 1=5m2+c2 thus 5m1+c1=5m2+c2 ...A
From two we get c1 >c2...B
From A and B m1<m2 ..thus suff
Hence the answer is C
Hope this helps.

By a physics reasonning: As both lines pass by the same point (5,1) and as the slope represents the constant acceleration or deceleration between 2 points, we can see now that if each line passes by a second point that differs for both lines and that is defined by a rule such as Y interceptor of n > Y interceptor of n, we can conclude on the way that the 2 slopes are related one another.

By the mathematical approach: o For the line n : y = a(n)*x+b(n)
o For the line p : y = a(p)*x+b(p)

We know from (2) that b(n) > b(p)

and we have as well:
o 1 = a(n)*5+b(n)
<=> b(n) = 1-5*a(n)

You can also draw the lines on the x-y plane and find out that the slope of line n is always greater than that of line p (when both slopes are either negative or positive) if you take both statements together.

I don't get the algebraic method.. however I was thinking that if the points intersect, then the line originating higher, or sufficiently lower than the other would result in a greater slope (assuming the slope can be positive or negative). But, if the y intercept for n is +1 and the y intercept for point P is -5, isnt the slope greater for P?

At first it was straight C, until I drew a picture on my scrap paper and realized that a higher Y intercept doesn't seem to necessarily mean a greater slope.