If lines k and j are in the xy coordinate plane, is the

Question

If lines k and j are in the xy–coordinate plane, is the slope of line k greater than the slope of line j ?

(1) The x-intercept of line k is greater than the x-intercept of line j 
(2) Lines k and j intersect at (7, 2)

Bunuel · Accepted Answer

Sorry to disappoint you guys, but it seems that the answer should be E.

First of all, to solve this question, think that the best way is the graphic approach:

We all agree that (1) and (2) alone are not sufficient.

Let's combine --> draw only the X-axis. The k intercept is greater than the j intercept --> the k intercept (k1) point is right to the j intercept point (j1) --> The interception of lines is above the X-axis (point 7;2) --> it will give us only three possible ways to draw the lines:

the slope of k > slope of j

the slope of k < slope of j

the slope of k > slope of j

So (1)+(2) is not sufficient. Answer E.

BUT the way you were solving also should get E:

f(k) = mx + n
f(j) = tx + p

(1) The x-intercept of line k is greater than the x-intercept of line j --> 0 = mx + n; 0 = tx + p --> -n/m > -p/t or n/m < p/t --> not sufficient.

(2) Lines k and j intersect at (7, 2)

2 = 7m + n; 2 = 7t + p --> 7m + n = 7t + p --> not sufficient.

Combining the way you did:
n = 2 - 7m --> n/m = 2/m - 7
p = 2 - 7t --> p/t = 2/t - 7

n/m < p/t --> 2/m - 7 < 2/t - 7 --> 1/m < 1/t --> (t - m)/(mt) < 0

And here is the catch, from the above statement, you cannot determine whether m > t or not. (t = 1) < (m = 3) statement is true and (t = 1) > (m = -3) statement is also true.

Answer E.

Economist · Answer

I get B but I am not sure. OA pls?
Following is the reasoning:
stmt 1: we just have two points on the x-axis. we can draw many lines via these two points and having different slopes. Insuff.

stmt2: we have the intersection point in the first quadrant. Now, draw a line perpendicular from (7,2) to the x-axis. This will be a vertical line. Now select two points on the axis just to right and left of (7,0) on x-axis. Let these points be the x-intercepts of the lines. Now the slope of line with a greater x-intercept say, (7.0001, 0 ) will always be -ve   and the slope of the line with a smaller x-intercept say (6.9999, 0 ) will always be +ve

Suff.

maliyeci · Answer

Approach of economist is nice. Lets do it more mathematically.
1)insuff. No need to explain.
2)insuff. No need to explain.

together
line k=> y=mx+n
line j=> y=tx+y
we know from 1 that n is greater than y. And we know from 2 that they are intersecting at point (7,2).
That makes
2=7m+n
2=7t+y
7m+n=7t+y
7m+n<7t+n
7m<7t
m<t

SUFF.
C.

mrsmarthi · Answer

Maliyeci,

I have two questions -

In y = mx + b equation, m = slope and b is the Y intercept. From your represenation, how can we say that

maliyeci

we know from 1 that n is greater than y.

when variables n and y are the Y intercepts. Not X intercepts.

Can you please explain how you made this Inequality based on n > y(assuming y intercepts of L > y intercept of K). I am confused. :roll:

maliyeci

7m+n<7t+n
7m<7t
m<t

maliyeci · Answer

I beg your pardon for the intercepts. Yes you are rigth. I gave the Y intercept. The x intercepts are respectively; 
-n/m and -y/t
But they are sufficient to find an answer.
That is the solution.
7m+n=2
n=2-7m
n/m=2/m-7
same as for the other
y/t=2/t-7
since -n/m is greater than -y/t; y/t is greater than n/m
so
2/m-7>2/t-7
2/m>2/t
so we can find the solution
C is suff.

mrsmarthi · Answer

Yes....this is correct. But with a small correction.

hgp2k · Answer

This exactly why I said IMO E

. Thanks for explanation Bunuel! :beer

imhimanshu · Answer

Hi Bunuel,

Request you to please look at the colored portion again and confirm if its correct. Isn't in Option A->Slope of j > Slope of K. If not, please provide your reasoning, may be I'm lacking some concept.

thanks

Bunuel · Answer

A steeper incline indicates a higher absolute value of the slope. So, if both lines have positive slope, then the line which is steeper has greater slope. If both lines have negative slope, then the line which is steeper has greater absolute value slope, its slope is "more negative", so less than the slope of another line. Similar questions to practice: if-the-slopes-of-the-line-l1-and-l2-are-of-the-same-sign-is-126759.html slopes-of-m-and-n-124025.html line-n-and-p-lie-in-the-xy-plane-is-the-slope-of-the-line-30553.html lines-n-and-p-lie-in-the-xy-plane-is-the-slope-of-line-n-97007.html in-the-xy-plane-is-the-slope-of-line-l-greater-than-the-126941.html Hope it helps.

jlgdr · Answer

I would solve algebraically.

Say line K is mx+b while like J is nx+c.

Question is is m>n?

Statement 1 tells us that -b/m>-c/n, but we know nothing about the signs of b and c hence insufficient.

Statement 2 says that 7m+b=7n+c, we could factorize to get m-n=c-b/7. Now question is is c-b>0? We don't know this.

Now from both statements together we still don't know whether c>b, so E is the best answer choice here.

Hope this gives a hand
Cheers!
J

Lucky2783 · Answer

Answer: E

refer to images attached.

arnkaprx · Answer

Can't we also use the formula - m = y2-y1/x2-x1 here? By that we get slope for line k = 2-0/7-x1 and slope for line j is = 2-0/7-x2. And since (1) says that x2 > x1, we can say that m(j) < m(k)? And thus C.

Abolnasr · Answer

This question is best approached by visually thinking about slope as if it's the physical steepness of a road, lines (roads) can fulfill both conditions with either one of them steeper than the other.

If lines k and j are in the xy coordinate plane, is the

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