If m represents the slope of a line in the coordinate geom

Question

If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1.  |m|= m 
2.  m^2=3m

Bunuel · Accepted Answer

Theory: 1. If the slope of line is negative , line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, line intersects the quadrant I too, if negative quadrant III. 2. If the slope of line is positive , line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV. 3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants . Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants. 4. If a line is horizontal the line has slope 0, is parallel to X-axis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect. 5. If a line is vertical , the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is x=a, where a is x-intercept. Similar questions to practice: in-the-xy-coordinate-system-do-any-points-on-line-k-lie-in-127635.html in-the-rectangular-co-ordinate-system-shown-does-the-line-k-67693.html in-the-xy-plane-is-the-slope-of-line-l-greater-than-the-126941.html in-the-xy-plane-if-line-k-has-negative-slope-and-passes-135197.html if-the-slopes-of-the-line-l1-and-l2-are-of-the-same-sign-is-126759.html lines-intersecting-angles-m08q15-66826.html#p1235093 lines-r-and-s-lie-in-the-xy-plane-is-the-y-intercept-of-lin-153952.html Theory on Coordinate Geometry: math-coordinate-geometry-87652.html DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41 PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

Zarrolou · Answer

If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1.  |m|= m  
So m is  \geq{ 0} . If m is 0, the line is straight, hence it can or cannot intersect the III quadrant.
Consider  y=-100  (yes) and  y=100  (no)

2.  m^2=3m  
 m^2-3m=0  so  m=3  or  m=0 . If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.

1+2)  Since m=0 is common, both statements are still not sufficient

WholeLottaLove · Answer

Two questions:

First, in #1 you said that if the slope is  negative  100 it intersects III but in #2 you said if it is  positive  3 it intersects III. Doesn't the sign change mean it intersect different quadrants?

Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer?

Thanks!

WholeLottaLove · Answer

If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. |m|= m 
M>=0

The slope could be equal to zero in which case the line runs flat along the x axis and does not pass through QIII.

The slope could be equal to 5 in which case the line would pass through QIII at some point.
INSUFFICIENT

2. m^2=3m

M^2 - 3m = 0

m=0, m=3. As with above, if m=0 it will not pass through QIII but if m=3 then it will.
INSUFFICIENT

1+2 
#1 tells us m>=0 and #2 tells us m=0 OR m=3 which is redundant when considering #1. Therefore, m may or may not pass through QIII.
INSUFFICIENT

(E)

Bunuel · Answer

Please read this post: if-m-represents-the-slope-of-a-line-in-the-coordinate-geom-155176.html#p1241612 Next, when considering the statements we have that m=0, which means that the line is horizontal. The question is "does the line intersect quadrant III?" not what is the value of m. Horizontal line may or may not intersect quadrant III. Hope it's clear.

Zarrolou · Answer

I think you are confusing the parts of the equation of the line.
 y=Slope(=m)*X+k <== this is the standard for of a line.

These two lines have NO SLOPE (they are straight, horizontal, parallel to the x-axis) => m=0.
 y=-100   y=100 . y=-100 is a straight line that passes through the III and IV quadrant; y=100 passes through the I and II quadrant.
(refer to the image)

If we know that m=0 both y=100 and y=-100 are still valid.

WholeLottaLove · Answer

Ahhh. It's been a while since I've done anything related to coordinate geometry (trying to nail modules down cold haha!) Now I remember. Thanks.

WholeLottaLove · Answer

This is an updated version of my original solution found above.

If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?

1. |m|= m 
M>=0

If m = 0 then it has no slope. However, it still may or may not pass through QIII. If y = 2 then it would be a flat line passing through QI and QII. If y = -2 then it would be a flat line passing through QIII and QIV. Furthermore, if the line did have a slope, it may or may not pass through QIII. For example, if it had a slope of 2 it would pass through QIII (assuming it has infinite length) but if the slope was negative it may not ever pass through QIII)
INSUFFICIENT

2. m^2=3m

M^2 - 3m = 0

m=0, m=3. If the slope is zero then it may or may not pass through QIII. We would need to know it's y coordinate to determine that. If the slope is positive 3, then it would pass through QIII
INSUFFICIENT

1+2 
Both 1 and 2 tell us that the slope could be zero or greater than zero. If the slope is zero then it may or may not pass through QIII. If it is greater than zero it will. We cannot determine if it passes through QIII or not.
INSUFFICIENT

(E)

WoundedTiger · Answer

Hi Zarrolou,

St1 |m|= m can also be inferred as |-m|=|m|= m since |-m|=|m|

this implies m>/ 0 or m <0

Combining with statement 2 we get m=0 as common and again answer can be yes or no depending upon value of y.

Will the above interpretation of st1 will be correct.

thanks
Mridul

Bunuel · Answer

No, that's not correct.

|m|=m  implies that  m\geq{0}  ONLY. What does m>/ 0 or m <0 even mean? It gives all values possible, doesn't it?

Absolute value properties:

When  x \leq {0}  then  |x|=-x , or more generally when  some \ expression\leq{0}  then  |some \ expression|={-(some \ expression)} . For example:  |-5|=5=-(-5) ;

When  x \geq {0}  then  |x|=x , or more generally when  some \ expression\geq{0}  then  |some \ expression|={some \ expression} . For example:  |5|=5 .

AmritaSarkar89 · Answer

My 2 cents for this long discussion.
statement 1= |M|=M
in this case m can be 0 or +ve or -ve
NS

Statement 2= m^2=3m
hence m can be 3 or 0 NS

Combining M can be +ve or 0 thus E is the correct answer.

UdaySJha · Answer

Statement 1.  |m|= m 
Analyzing the modulus : |Any number|= either 0 or +
That implies the value of m can be either 0 or +
Now if the slope of a line is either 0 or +, it can intersect or not intersect Quadrant III.
As Slope = Change in y/change in X
Scenario A: if ^y =+ and ^X=+, slope =+ ; Slope will intersect 
Scenario B: if ^y =- and ^X=-, slope =+ ; Slope will intersect 
Scenario C: if ^y =0 and ^X=-, slope =0 ; Slope will not intersect

So, It is not sufficient.

Statement 2.  m^2=3m  
This statement also implies m is either + or 0 as product of a positive no. and a variable is equal to a square number.
Therefore again it is a restatement of earlier 1. So, It is also not sufficient.

Therefore , Answer E.

BrentGMATPrepNow · Answer

Target question :    Does the line intersect quadrant III?  
Jump straight to...

Statements 1 and 2 combined    
Here are two scenarios that satisfy BOTH statements: 
 Case a : m = 3 
 https://i.imgur.com/2SVui9E.png 
In this case, the answer to the target question is  YES, the line DOES intersect quadrant III

Case b : m = 0. 
 https://i.imgur.com/5nreIQ1.png 
In this case, the answer to the target question is  NO, the line does NOT intersect quadrant III

Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

itsarudolf · Answer

Hey guys,

it is probably obvious to the most of you, but why can't we just reduce the equation in 2 by m and have m = 3? Could it be possible if the stem mentioned any additional information?

Cheers
Rudolf

rvgmat12 · Answer

Official Explanation:
If a line has a positive slope, then it must go through quadrants I and III in the coordinate geometry plane. Once that is established, this problem is more of a positive/negative number properties question. In other words, can the sign of m be determined from the information in the statements. Statement (1) guarantees that m is either positive OR zero. If a line has a slope of zero, then it is a horizontal line such as y = 5 which does not go through quadrant III. However, it could also be a line with a positive slope that does go through quadrant III so statement (1) is not sufficient. Statement (2) is a quadratic equation with two solutions. Setting all terms equal to 0, it is shown that m2 - 3m = 0 or m(m - 3) = 0 and m = 3 or 0. Again, this information is not sufficient because m could be positive or zero, yielding the same possibilities as statement (1). Putting the statements together, there is still ambiguity of whether m is 0 or positive, so the answer is E, both statements together are not sufficient.

bumpbot · Answer

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If m represents the slope of a line in the coordinate geom

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If m represents the slope of a line in the coordinate geom

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