Does line y = mx + c intersect X axis?

Question

(1) m < 0
(2) c > 0

AmrithS · Accepted Answer

Statement 1 Alone:
It is given that the slope of the line is negative. Thus, at one point or other, it will intersect the x-axis.

The point at which it will intersect the x-axis is:

mx + c = 0 or x = -c/m

SUFFICIENT

Statement 2 Alone:
It is given that the y intercept is greater than 0. This means that the line intersects the y axis at a point y>0.
It is not necessary for the line to intersect the x-axis because the line can be parallel to the x-axis while having a positive y intercept

Ans: 'A'

Gnpth · Answer

Statement 1 : M<0 means slope is negative, so at some point the line will intersect x. intersection point : mx+c=0, so x= -c/m... (A is sufficient) Statement 2: y intercept is greater than 0, so it will intersect y>0. This line may be parallel to x-axis with positive y intercept.. so not sufficient. Answer is A

Hope it is correct. i guess i came across this problem earlier :lol:

in Club forum :!:

jellybean23 · Answer

+1 Kudos.... :wink:

Thanks a lot !!! :-D

Any idea is if we have a quadratic equation f(x)=Ax^2+C=y will this intersect with x axis if we know that A<0 or C>0??

Bunuel · Answer

Check here for theory: math-coordinate-geometry-87652.html Hope it helps.

visheshchadha · Answer

The first statement (m<0) alone is sufficient to answer but not the second statement (c>0) alone.

The reason is that if m=0, then the line is parallel to Y-axis, hence won't intersect the X-axis. Since m<0, it is a line with decreasing slope, hence the line will intersect and cut the X-axis at a certain stage.

As for the statement 2 (c>0), it may or may not intersect the X-axis as the line may be parallel to X - axis and still have a positive c. Example : y = 5 is a straight line with c = 5 >0 and won't ever cut the X-axis.

sanaexam · Answer

mx + c = 0 or x = -c/m
.pls explain this part.pls

Bunuel · Answer

mx + c = 0;

mx = -c;

x = -c/m.

sanaexam · Answer

y=mx+c.how did y become 0?

Bunuel · Answer

x-intercept is the value of x for y = 0. Check here for theory: math-coordinate-geometry-87652.html

sanaexam · Answer

ok.now understood:)

MDUsman · Answer

if it is a parallel line to x axis as assumed in option b then why are we assuming it to follow the formula.
Can't the formula be y=c then instead of y = mx+c

kop18 · Answer

I have a doubt with this question-

If I assume that in y=mx+c; c=0 then can we not assume that the line can be of the form (y=-x) i.e. y= -x+ 0 then A is not sufficient because if the line is defined as y=-x it passes through origin and never intersects the x axis, giving a "no" to the prompt. However, if C is not 0 then the arguments mentioned above are correct and it gives a "yes" answer to the prompt. 
Therefore, giving a yes/no answer to the question stem.

Please could someone help?

Bunuel · Answer

The origin, (0, 0), is also a part of an x-axis.

Does line y = mx + c intersect X axis?

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Does line y = mx + c intersect X axis?

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