Coordinate Geometry

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Coordinate Geometry

by clinton » Mon May 30, 2011 5:30 am
Could someone lend a helping on this question. The coordinates for the line L is (0,3) and (6,0). I tried to provide a visual but it didn't comeout correctly:


All points (x,y) that lie below the line L, shown above, satisfy which of the following inequalities?

1.) y < 2x + 3

2.) y < -2x + 3

3.) y < -x + 3

4.) y < 1/2x + 3

5.) y < -1/2x + 3
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by MBA.Aspirant » Mon May 30, 2011 5:39 am
5) y < -1/2x + 3

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by clinton » Mon May 30, 2011 5:41 am
How'd you get the answer?

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by galaxian » Mon May 30, 2011 6:15 am
Image

If you consider the above shaded portion as the required area,

Line's Equation would be :
y = -1/2x + 3
but for area under the line, it would be y < -1/2x + 3.Hence (E)

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by SoCan » Mon May 30, 2011 7:05 am
Line equation is y=mx+b, where m is the slope and b is the y-int. Coordinate (0,3) gives 3 as b. Slope is (0-3)/(6-0) = -1/2. So the equation for the line is y=-(1/2)x+3.

However, the question asks for the inequality that represents the points below that line, so it is y<-(1/2)x+3

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by itsmebharat » Sun Jun 05, 2011 12:01 am
coordinates for the line L is (0,3) and (6,0), we have to find the equation of Line L

Step 1: Find the slope of the Line L,
Slope = Rise/ Run ==> m = (3-0) /(0-6) =-1/2

So, m = -1/2

Step 2 : Find b, by putting any of the coordinates provided. let say, (0,3)

eqn of line is , y = mx +b
x =0, y =3 ==>

3 = (-1/2)*0 + b ==> b=3

Step 3 : put the value of m and b in the equation , y=mx+b,

y = (-1/2)x + 3

As the ques ask for All points (x,y) that lie below the line L, shown above, satisfy which of the following inequalities?
[spoiler]hence the result is E, which says 5.) y < -1/2x + 3[/spoiler]
I am not an Expert, please feel free to suggest if there is an error.

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by cans » Sun Jun 05, 2011 1:21 am
The coordinates for the line L is (0,3) and (6,0).
All points (x,y) that lie below the line L, shown above, satisfy which of the following inequalities?

1.) y < 2x + 3

2.) y < -2x + 3

3.) y < -x + 3

4.) y < 1/2x + 3

5.) y < -1/2x + 3
Line L: (0,3),(6,0) y-intercept=3 and slope=(3-0)/(0-6) = -1/2
y=(-1/2)x + 3
Thus all points lying below the L should satisfy y < (-1/2)x + 3
IMO E
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by sandeep800 » Sun Jun 05, 2011 10:37 am
Thanx Cans
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