In the xy-plane, if line k has negative slope and passes through the point (-5,r) , is the x-intercept of line k positive?

(1) The slope of line k is -5.
(2) r > 0

Thanks a lot, as usual this is solid solution. Question: My problem was visualising the line I guess, I see with negative slope and r (y coordinate) being posiive, only second quardant is possible .I miss some point I guess.. COuld you give me idea of two angles of two lines from x_axis to visualise better ? sorry, but I miss some basic points I guess.

Thanks Bunuel. You bring me luck, you speak and problem is solved.

I meant that i was not able to visualise two cases where x intercepts could be positive or negative , but I can not. I did dig a little in lines and got the answer.

Thanks again for iron proof answer by you.

P.S. I am going to review/attempt all Qs and concept on number properties by you as this is an area I need more confidence. wil hear more from me. My exam is roughly in four weeks.

yes, good way too Gurpreet.
lets play with it further to strenghtne the concepts .

If I modify the second statement to

2. r < 0 ,

let's try to solve it in two ways i.e. First by visualising it and second, by using the basic equation y = mx +c

Using the second method,

The equation is r = 25+c and we know r < 0, so only possibility is c < -25 , so this can tell definitely the answer. Am I correct ?
But if we want to visualise it, is there any possibility it can pass through First quadrant ? Second quadrant i can imagine easy .

Also, How a line can make more than 180° angle ? I am from good maths background but do not remember exacly how a line makes more than 180° . So little help will break the code.

Let's take it a step further.
Adding one more question that will take discussion further . (Source: GMATprep)

Lnes 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.

1. Clearly insufficient : For equation n y=m1.x+c1 and for equation p y=m2.x+c2 =>
First equation of line :1 = 5.m1+c1
Second equation of line: 1= 5.m2+c2

Clearly, m1 and m2 Can take any vset of values that m1>m2 and m1<m2, both are possible

2. Insufficent again : y=m1.x+c1 and y=m2.x+c2 => given is c1 > c2 => m1 and m2 can take any set of values again

1 and 2 statement togather :

First line : 1 = 5.m1+c1
Second Line: 1= 5.m2+c2

From this we can conclude that 5.m1+c1 = 5.m2+c2 or 5 (m1 - m2) = c2 - c1
now we are given c1 > c2 , I beleive that Statement refers to absolute values so
c1 could be 4 and c2 as 3 => c2-c1 gives -1
or c1 could be -4 and c2 as 3 => c2-c1 gives 7
or c1 could be 4 and c2 as -3 => c2-c1 gives -7
or c1 could be -4 and c2 -3 => c2-c1 gives 1

that means m1 and m2 can be greater or lesser than each other.So both together not sufficinet.

If I ignore my assumption that the values are absolute :
In that case, c2-c1 has to be negative if c1 > c2 . so m1 - m2 has to be negative too .

m1 - m2 < 0 or m1 < m2 , Sufficient

Question 1 : Which of the case one should assume ? answer is C that both together are sufficient that means we can't assume absolute values.

Question 2 : Sloe -1 and slope -2 , generally speaking -1 is greater than -2 but slope if we look at -2 is greater than -1.

What is the rule one should follow ?

I still cant visualize.

In stmt 2: we know that like passes through second quadrant and it has negative slope. How can it intercept at positive x?

Negative slope always goes bottom to top from left to right.

Please help me visualizing this, I am sure i am missing something.

@testprep2010 : Your response is E. I do not understand what values such posts bring.

1. This is OG question so answer is known.
2. The post does not just ask to answer just an option
3. How do I know your answer is wrong or right ?
4. Even if everyone votes A for this, it will not change the answer.

I feel sad why people put thier time answering like this on these forums.

Thanks Bunuel.. for the Kudos! A kudos from u.. means a lot!
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The question stem tells you that line k has negative slope so m < 0.

Also, you may want to look at the diagram made by jeeteshsingh in the first reply to this question. It uses both the statements together and shows you two possible cases (through two different dotted lines). In one case, line k has positive x intercept; in the second case it has negative x intercept. Hence both statements together are not sufficient.
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'm' is the slope of the line in the equation y = m*x + c
The question stem already states that the line has negative slope. Hence, m < 0.