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Re: do any points on line k lie in quadrant III? [#permalink]

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31 Oct 2009, 04:25

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Okay, this is about 'imagination' You are told in stmt 2 that the slope is positive. 1. draw a line with positive slope passing thru origin ( does it go thru Q3 ? - yes ) 2. draw a line with positive slope passing thru ( 7, 0) ( does it go thru Q3 ? - yes ) 3. imagine a line with positive slope passing thru ( 1000, 0 ) ( does it go thru Q3 ? - yes ) ..it cant be plotted on paper but yes for some -ve y-intercept is surely will go thru Q3.

Re: do any points on line k lie in quadrant III? [#permalink]

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31 Oct 2009, 08:47

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Here is a way I use to imagine the slopes (i think it'll help an outdoor person who's math sucks as bad as mine!)

Positive slope... it is an incline, I can climb. Negative slope... no way I can climb this slope (unless I have the Cliffhanger training) 0 - ah okay, plain straight line, just walk infinite - up against a wall

So in this particular context, positive slope wherever it is drawn, will pass through IIIrd quadrant... well I had a tough time remembering quadrants.

Hey guys..I got this question wrong b'cos I did'nt know HOW to plot the line when ONLY the slope is given.. Can somebody help me with that please?!

tejal777, below are my notes and tips about the slope of a line and the quadrants of intersect of a line depending on a slope. Hope you find them useful:

The slope is defined as “rise over run,” or the distance the line runs vertically divided by the distance the line runs horizontally. The slope of any given line is constant over the length of that line. Given any two points on the line, take the difference between the y (or vertical) coordinates and divide that by the difference between the x (or horizontal) coordinates.

Equation of a line y=mx+b: slope m, b Y intersect. OR Equation of a line ay+bx+c=0: slope -b/a, -c/a Y intersect.

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.

6. For the line crosses the two points (x1,y1) and (x2,y2), slope m=(y1-y2)/(x1-x2)

7. If the slope is 1 the angle formed by the line by X and Y axis is 45 degrees.

8. If the slope of a line is m, the slope of a line perpendicular to it is its negative reciprocal, -1/m. Hence two lines are perpendicular if and only the product of their slopes is -1.

9. Parallel lines have same slope.

10. Given a point and slope, equation of the line can be found. The equation of a straight line that passes through a point (x1, y1) with a slope m is: y - y1 = m(x - x1)
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In the xy-coordinate system, do any points on line k lie in quadrant III?

(1) Line k has y-intercept 2

(2) Line k has slope 2/3

please explain the answer

For the line to be in the III quadrant the slope of the line y = mx+c that is m should be positive.

Statement A: Tells us that y-intercept is 2. Y-intercept means point where x is zero. Hence when x=0, y=2 in the line y=mx+c =>c = 2. This statement does not give us the value of m (slope of the line). Hence insufficient.

Statement B: Line K has slope 2/3. Given m = 2/3 which is +ve and hence some point of the line k should lie in the III quadrant.

Sufficient. Hence B is the answer.
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so in III and I quadrant slope will be positive and in II and IV quadrant slope will be negative ?

Yes, but the wording should be spot on since there are minor twists to the rule.

Rule:

SLOPE AND QUADRANTS:

1. If the slope of a line is negative, the 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, the line intersects quadrant I; 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.

Re: In the xy-coordinate system, do any points on line k lie in [#permalink]

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Re: In the xy-coordinate system, do any points on line k lie in [#permalink]

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04 Dec 2014, 02:49

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Re: In the xy-coordinate system, do any points on line k lie in [#permalink]

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