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Re: The graph of which of the following equations is a straight line that [#permalink]

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21 Oct 2015, 23:22

3

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Vyshak wrote:

One of the lines parallel to the given line will have co-ordinates (3,-2). Substitute x = 3 and y = -2. option B satisfies the equation.

Answer: B

the slope of the given line is +ve. so you need another +ve slope line to be parallel to it. Only options A and D have that. Out of which only option a matches with the slope of 2/3 of line l. so A.

The graph shows that the line passes (-3,0) and (0,2). So the difference of x is 3(=0-(-3)), the difference of y is 2(=2-0). The gradient of the line is, therefore, 2/3.

A parallel line should have the same gradient. Among the chioces only (A) has the gradient 2/3 (3y-2x=0 --> 3y=2x --> y= (2/3) x). So the answer is (A).
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A line is parallel to line l if it has the same value for m in the formula y=mx+b. So we have to calculate the value of m of the line l in the picture:

y2-y1/x2-x1 = 2-0 / 0-(-3) = 2/3 =m = slope of line l

If you rewrite (A) to y = 2/3x, you see that A has the same slope.

Answer A.
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Re: The graph of which of the following equations is a straight line that [#permalink]

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06 Nov 2015, 22:22

I'll go with A. For the lines to be parallel, the slope must be the same for the perpendicular lines, the slope of the second line is the negative reciprocal of the slope of the first line. Here, we are looking for a line with the same slope as the drawn line - 2/3 only A has the same slope.

Based on "Observation 1" Options B, C and E are ruled out

Now, Options A and D remain

Based on Observation 3, Option D is ruled out which has slope=3/2

Answer: Option A

P.S. Observation 2 in this question was not necessary as we had to find a line parallel to given line for which Y-Intercept must be different. But these are critical and Primary observations that one must make before starting to solve in question of Co-ordinate Geometry _________________

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The graph of which of the following equations is a straight line that [#permalink]

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07 Nov 2015, 08:20

Clearly, the line passes through (0,2) and (-3,0). The slope for this line : 2/3. A line parallel to this line will have the same slope. So, option(A) is having the slope as 2/3.

Based on "Observation 1" Options B, C and E are ruled out

Now, Options A and D remain

Based on Observation 3, Option D is ruled out which has slope=3/2

Answer: Option A

P.S. Observation 2 in this question was not necessary as we had to find a line parallel to given line for which Y-Intercept must be different. But these are critical and Primary observations that one must make before starting to solve in question of Co-ordinate Geometry

hi, even observation 1 is not necesary.... parallel lines have the same slope so obsn 3 is sufficient..
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Based on "Observation 1" Options B, C and E are ruled out

Now, Options A and D remain

Based on Observation 3, Option D is ruled out which has slope=3/2

Answer: Option A

P.S. Observation 2 in this question was not necessary as we had to find a line parallel to given line for which Y-Intercept must be different. But these are critical and Primary observations that one must make before starting to solve in question of Co-ordinate Geometry

hi, even observation 1 is not necesary.... parallel lines have the same slope so obsn 3 is sufficient..

It is necessary to rule out B,C,E for their slopes are <0

Either you actually calculate the slope to rule out B,C,E or just look at the positive nature and rule these 3 options out.

hi, even observation 1 is not necesary.... parallel lines have the same slope so obsn 3 is sufficient..

It is necessary to rule out B,C,E for their slopes are <0

Either you actually calculate the slope to rule out B,C,E or just look at the positive nature and rule these 3 options out.

Hi, I think its very straight.. if one observation can eliminate all wrong choices, other observations are not necessary.. arent you required to check for slope.. if any other set of line ,other than llel lines, also has property of same slopes, only then you may require to use other obsn to eliminate choices..
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The graph of which of the following equations is a straight line that [#permalink]

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13 Feb 2016, 19:33

Another way to look at slope can be to interpret it visually by noticing the transition through its two points (intercepts): when y increased by 2 (from 0 to 2), x increased by 3 (from -3 to 0), therefore slope = 2/3.

Okay here is a very simple solution but you must understand that slope = rise or drop in y axis/run of x axis.(always take absolute value of x) Now here slope = rise/run=2/3. Parallel line will also have same slope. Check A bcz it is the easiest to check for. ... well we have a slope of 2/3. We don't even have to look at any other option. Answer is A Remember in PS there is only one unique solution to the problem.

Re: The graph of which of the following equations is a straight line that [#permalink]

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30 Dec 2016, 07:40

Please, if anyone could clarify my confusion I'd be thankful. In the given graph I have interpreted the coordinates as (0,2) and (-3,0). From my calculation the slope turns out to be 3/2 according to which the given option D's slope matches with the calculated slope.

Please, if anyone could clarify my confusion I'd be thankful. In the given graph I have interpreted the coordinates as (0,2) and (-3,0). From my calculation the slope turns out to be 3/2 according to which the given option D's slope matches with the calculated slope.

Please help me out!!

You should show your work. How else we can find an error in your calculations? What slope did you get? What is the slope of the line from option D? From option A?
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Re: The graph of which of the following equations is a straight line that [#permalink]

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30 Dec 2016, 22:36

Bhuvan.deshwal wrote:

Please, if anyone could clarify my confusion I'd be thankful. In the given graph I have interpreted the coordinates as (0,2) and (-3,0). From my calculation the slope turns out to be 3/2 according to which the given option D's slope matches with the calculated slope.

Please help me out!!

For the given line, slope should be 2/3. for an equation of line ax +by +c =0, the slope m=-(a)/b.

--find the equation of the given line

x/(-3) +y/2=1 2x-3y+6=0

so, m =2/3

Hope it helps.. If it does not, as Bunuel said, you have to tell how are getting slope 3/2.

The slope of the given line in slope-intercept form is y=(2/3)x +4 parallel lines have same slope, so of all the given option only one equation has slope = 2/3.