In xy-coordinate plane, lines j and k intersect at the point (5, 0)

Question

In xy-coordinate plane, lines j and k intersect at the point (5, 0). If both lines have defined slopes, is the y-intercept of line j greater than the y-intercept of line k?

1) The slope of line k is greater than the slope of line j. 
2) Line j has a negative slope

*kudos for all correct solutions

BrentGMATPrepNow · Accepted Answer

Target question :    Is the y-intercept of line j greater than the y-intercept of line k?

Statement 1 : The slope of line k is greater than the slope of line j.   
Let's examine 2 cases: the slope of line j is positive and the slope of line j is negative 
 Case a : the slope of line j is positive
 https://i.imgur.com/JzxWnbh.png 
Notice that, if line k has a greater slope, then  the y-intercept of line j IS greater than the y-intercept of line k

Case b : the slope of line j is negative
ASIDE: Some students will misinterpret statement 1 to suggest that line k is steeper than link j. However, this is true ONLY WHEN line j has a positive slope. The opposite is true when line j has a negative slope. 
To help visualize this, I have made slope of line j equal to -1
 https://i.imgur.com/SCzlRly.png 
Notice that a slope of -2/3 is greater than a slope of -1
And a slope of -1/8 is greater than a slope of -1
As we can see, in all cases,  the y-intercept of line j IS greater than the y-intercept of line k

Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : Line j has a negative slope  
This statement is NOT sufficient. 
Consider the following two cases:
 https://i.imgur.com/wL61mDX.png 
In the above case,  the y-intercept of line j is GREATER than the y-intercept of line k

https://i.imgur.com/JISFxny.png 
In the above case,  the y-intercept of line j is LESS than the y-intercept of line k 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

chetan2u · Answer

Hi...
Statement I tells us that slope of k is more than that of J..
Slope is nothing but change in y/change in x.
Since both intersect at one point, with given info we can find relation, not the numeric difference, of y intercept with each other
Suff
Statement II talks only of one linee
Insufficient

A

rt9 · Answer

how is A the answer?
if J has negative slope and K negative slope then y intercept of k is greater.
if J has positive slope and K positive slope then y intercept of j is greater.

Anannt · Answer

Ans :A
St 1: Slope of line K > Slope of line J
There are three cases
1. Both lines have - ve Slope
Y intercept of J >Y intercept of K
2 Both lines have +ve Slope
Y intercept of J > Y intercept of K
3 One line +ve and other - ve
Y intercept of J >Y intercept of K

All three cases gives same answer, hence St I sufficient

St II line J has - ve Slope

If both lines have - ve Slope and 1 Slope of line K > Slope of line J
Y intercept of J >Y intercept of K
2 Slope of line K <Slope of line J
Y Intercept of J < Y intercept of k

Sent from my Mi 4i using GMAT Club Forum mobile app

Kinshook · Answer

It is required to find whether y- intercept of line j > y - intercept of line k when these line intersect at (5,0) in XY plane.

Let us assume equations of lines as:

Line j : y=m1x+c1
Since line j passes through (5,0)
0=5m1+c1=> c1=-5m1
Equation for line j becomes 
y=5m1 x-5m1

Similarly equation for line k can be written as
y=5m2 x -5m2

In the equation of line as 
y= m x + c, c is the y-intercept

Where m1 & m2 are slopes of line j & line k respectively

1. Given that m2>m1 => -5m1>-5m2
=> y-intercept of line j > y- intercept of line k . Sufficient

2. It can not provide data for comparison. Insufficient

There statement 1 alone is sufficient

IMO A

Posted from my mobile device

Pankaj0901 · Answer

Nice explanation. But, fundamentally, what I understood from your explanations are:
1. Slope= Angle between the line and the x-axis in the counter-clock wise direction. (Irrespective of slope being positive or negative.) 
2. Intercept= Actual value of y (with sign) and not the absolute modulus values, are considered. Example, y-intercept of -8 is less than y-intercept of 1, despite |-8|>|1|..

Hope my conclusions are right?

BrentGMATPrepNow · Answer

I agree with #2 (y-intercept = the actual value of the y-coordinate of the point that crosses the y-axis), but I don't agree with #1. 
I'm not even sure how you'd apply that definition to line k below: 
 https://s24.postimg.cc/pvchf54vl/image.png

Cheers, 
Brent

Pankaj0901 · Answer

Thank you, Brent. For point 1, could you please check the attachment: https://postimg.cc/LnWpqf57 slope of line l (-1/8) > slope of line k (-1) which is also equivalent to angle between positive x-axis and the line, along counter clock-wise direction.

Pankaj0901 · Answer

@Brent- Could you please validate this? Thanks in advance.
I have one more follow-up question:
A line (L1) with slope= -1 (135 degrees is the angle between Line L1 and positive x-axis, along the counter clock-wise direction with base as Positive x-axis)
A line (L2) with slope= 1 (45 degrees angle between Line L2 and positive x-axis, along the counter clock wise direction with base as Positive x-axis) 
Here, slope of L2 > Slope of L1.  Right? 
So, it would be basically: A line with positive slope will always have a greater slope than the line with a negative slope...?

QuantMadeEasy · Answer

Fdambro294 · Answer

If one wishes to talk an algebraic approach to the problem:

The Slope of a line is defined as ——>

(-) (Y-Intercept)
______________
(X-Intercept)

Let the equations representing each line be:

Line J: y = c(x) + J
—-where c = slope of line J
—-and J = y-intercept of line J

Line K: y = d(x) + K
—-where d = slope of line K
—-and K = y-intercept of line K

Question: is the y intercept of line J > y intercept of line K?

Rephrased - ***Is: J > K ?

Statement 1: slope of line K > slope of line J

Using the formula that

Slope = (-negative) (y-intercept) / (x-intercept)

And

The fact that both lines cross the X -Axis and intersect are point (5 , 0) ——> letting us know that each line’s X intercept = 5

Slope K > Slope J

>

—multiply both sides of inequality by positive +5

(-)K > (-)J

—multiply both sides of inequality by a negative value (-1), resulting in the inequality sign being REVERSED

K < J
or

J > K
Which, using the definition of the variables, means:

Y-intercept of line J > Y-Intercept of line K

Statement 1 sufficient alone

Statement 2 only tells us that line J has a negative slope

This ensures that Line J has a positive Y-Intercept (*RULE* for negative sloping lines that do not pass through the origin, the Y-intercept will have the SAME SIGN as the X-Intercept)

If line K has a positive slope, the line K’s Y Intercept will be negative and we will get a YES

if line K has a steeper negative slope than Line J, then Line K will cross the Y-Axis at a higher point in the positive direction. We will get a NO

Statement 2 NOT sufficient alone

*A*

Posted from my mobile device

Spanda3285 · Answer

For statement 1 it states the slope of line k is greater than line j can the slope of line j be negative while the slope of line K be positive?

Thank you in advance!

In xy-coordinate plane, lines j and k intersect at the point (5, 0)

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GMAT Data Sufficiency (DS) Questions

In xy-coordinate plane, lines j and k intersect at the point (5, 0)

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