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20 Jul 2021, 21:39
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A negative slope passes through which two quadrants? Please share reason.
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bansalgaurav
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20 Jul 2021, 23:30
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vipulg9
IMHO a line with a negative slope can pass through any two quadrants, that would depend on the equation of the line.
The most important point is signs of the X intercept and Y-intercept.
Note: If slope of a line is negative, is equal to = - y intercept/x intercept = {(y2-y1) / (x2-x1)}
If slope is negative, x intercept and y intercept has to be of the same sign.
for more clarity on slope pls do check this question:
https://gmatclub.com/forum/in-the-xy-pl ... 35197.html
21 Jul 2021, 00:33
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vipulg9
TIPS ON 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.
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 to either of axis crosses only two quadrants.
4. If a line is horizontal it has a slope of \(0\), 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 a line that crosses two points \((x_1,y_1)\) and \((x_2,y_2)\), slope \(m=\frac{y_2-y_1}{x_2-x_1}\)
7. If the slope is 1 the angle formed by the line is \(45\) degrees.
8. Given a point and slope, equation of a line can be found. The equation of a straight line that passes through a point \((x_1, y_1)\) with a slope \(m\) is: \(y - y_1 = m(x - x_1)\)
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For more check:
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Ultimate GMAT Quantitative Megathread
Hope it helps.
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