Is the slope of line l 0 A - The line passes through

Question

Is the slope of line l > 0 
A - The line passes through 3rd and 4th quadrant. 
B - The line passes through 1st and 4th quadrant. 

No OA. I have some thoughts...want the group to give their explanation.

carsen · Answer

B is the answer.

Pardon .. i had to edit the answer.  The answer is indeed C . I misread the statements. 

combing botht he statements we can plot the line and can see get information about the slope.

MA · Answer

OA is C.

i. if the line passes only through 3rd and 4th qd, the line is ll (parallel) to ox line and has 0 slope. but the question is silent about the line passes through 3rd and 4th or it also crosses other qd also. therefore i is insufficient.

ii. it is also the same. here, the slope is undefined.

However, combining i and ii, we know that the line passes through 1st, 3rd and 4th qd. therefore the slop of the line is not 0 or undefined.

batliwala · Answer

from i. the line can be parallel to x axis (slope =0), sloping upward (+ve slope) or downward (-ve slope)-Insuff
ii. also is insufficient on same reasoning parallel to y axis (slope undefined), sloping upward from left to right (+ve slope), sloping downward from left to right (-ve slope) .

C, combining we know that the line is having a positive slope and passing through 3rd/4th/1st quadrant and it sloping upward from left to right.

if the slope is undefined the line is parallel to Y axis, but this is not the case here. The line is inclined going up from the 3rd to 4th quadrant passing through the first quadrant ie.. it is sloping upwards with a positive slope

foraj · Answer

Without knowing two points on a line, it's not possible to find the slope of a line, the answer should be E.

ruhi · Answer

I'l go with C.

State. 1- Let (x1,y1) and (x2,y2)= (5,-5) and (-5,-10) slope=10/5=2>0

lets take (-3,-1) and (15,-7) slope= -18/6=-3<0

Hence, insuff,

State 2- 1) (12,3) and (1,-2), slope= 11/5>0
2) (5,5) and (10,-12) slope= -15/17<0
Hence, insuff.

Combining both,
1) lets consider the intercept form x/a+y/b=1 where a= intercept made on x axis, and b= intercept made on y axis.

LEts take a=5, b=-7, we get 5y=7x+35, hence slope=7/5>0
lets again take a=5, b=-10, we get y=2x+10, hence slope=2>0

Hence, suff.

Answer is C.

gayathri · Answer

C for me.

If a line passes through 1, 3 & 4th quadrant, its is rising from left to right, so it has a positive slope.

s  and s  are not suffiecient as you cannot determine the direction of the line, it could be parallel to one of te axes or may have an anagle.

foraj · Answer

If the line is passing through quadrant 1, 3 and 4, then the x and y intercepts could be x=3, y=2, equation will be x/3 + y/2 = 1, this gives you a slope of -2/3, which is negative, so we need exact two points or the exact intercepts.

ian7777 · Answer

this line will go through quadrants 1,2, and 4, not 1, 3, and 4.

batliwala · Answer

yep, agree with gayatri that the slope is positive rising upwards and passing through 3rd/4th/1st quadrant. I have edited my earlier post as I messed up with the order of quadrants.

batliwala · Answer

foraj you will not be getting a positive intercept for Y for a line passing through quad 1,3,4. Ian is right, for you example the line will be passing through the 1,2,4 quad.

Del231 · Answer

But do not you also have to determine the progression of relationship of x to y not just that it is positive or negative?

ian7777 · Answer

No. slope is just rise over run. Take any two points of a line that goes from down from left to right, and you'll get a negative slope. Doesn't matter which way you go, it'll be negative.

foraj · Answer

After some thinking i agree that if the line is passing through quadrants 1,3 & 4 the slope will always be +ve. 

Nice question vensune!!

pjk · Answer

By definition, a line extends infinitely in both directions. Hence, if it passes through Q3 and Q4, then it must be parallel to the X-axis. In this case, the slope, defined as the ratio of rise to run, is zero. Hence, st I is sufficient. Using the same reasoning, if a line passes through Q1 and Q4, it must be parallel to the Y axis. In this case, the slope is undefined, and I tend to think that it is also sufficient to answer the question.

Since, this explanation is contrary to the above discussion, am I missing some concept?

venksune -- (i) good question, and (ii) yr thoughts please..

pjk

venksune · Answer

I also have C. Just wanted to get the opinion. Thank all you guys..

here is my notes..
1. lets take (-3,-4) and (4,-5) - which is a line that's in the III and IV th quadrant. Slope = (y1-y2)/(x1-x2) = (-4+5)/(-3+4) which is >0. However if the co-ordinates are (-6,-4) and (4,-5) the slope is (-4+5)/(-6-4) which is 0 .  The line can be parallel to y axis and the slope of vertical lines is undefined . So, Insuff.

Combining both we know that its not ahorizontal line or a vertical line and that it is a line that is cutting across 1st, 4th and 3rd quandrants. Clearly the slope of the line is not 0 or undefned. Howeer, since the slope is passing from 3rd to 4th to 1, it is positive. So, C.

Is the slope of line l > 0 A - The line passes through

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