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Re: If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 06:50
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2
If line passes through (31,22) and (48,33), it means that for every increase of 17 of x (48-31), y will increase by 11 (33-22). We want to know the value of x when y is zero so let's decrease y by 11 at a time, which will decrease x by 17 at a time. This means the line will pass through: (31-17, 22-11) which is (14,11) and (14-17,11-11) which is (-3,0).
Answer is B
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If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 07:35
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GMATPrepNow wrote:
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?
A) -25 10/11 B) -3 C) -1 16/17 D) 1 16/17 E) 25 10/11
*kudos for all correct solutions
Equation of the line k passing through given vertices: y-33=m(x-48)where m=11/17 (General form of equation of line passing through two points (x1,y1) and (x2,y2):- y-y1=m(x-x1)) and m=slope=(y2-y1)/(x2-x1) At x intercept ,y=0. So,we have -33=(11/17)(x-48) Or, x-48=-51 Or, x=-51+48=-3 (please note this is the x-intecept point because we have determined x at y=0)
Ans. (B)
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If line k passes through the points (48, 33) and (31, 22),
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Updated on: 09 Jul 2018, 08:26
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m (slope) = \(\frac{(y2 − y1)}{(x2 − x1)}\)
We have to determine the coordinate of the point where this line intercepts x-axis but the coordinate of y at this point is equal to 0.
Hence if we plug in the values of the two points as provided in the question stem & equate in the aforesaid formula we get the value of x intercept as -3
Hence option B is the correct answer.
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Originally posted by CAMANISHPARMAR on 09 Jul 2018, 08:06.
Last edited by CAMANISHPARMAR on 09 Jul 2018, 08:26, edited 1 time in total.
WE: Supply Chain Management (Energy and Utilities)
Re: If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 08:17
CAMANISHPARMAR wrote:
The "point-slope" form of the equation of a straight line is:
y2 − y1 = m(x2 − x1)
Therefore m = \(\frac{(y2 − y1)}{(x2 − x1)}\)
We have to determine the coordinate of the point where this line intercepts x-axis but the coordinate of y at this point is equal to 0.
Hence if we plug in the values of the two points as provided in the question stem & equate in the aforesaid formula we get the value of x intercept as -3
Hence option B is the correct answer.
Hi Manish, Please check the equation of line in 2 point form .
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PKN Rise above the storm, you will find the sunshine
Re: If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 08:25
PKN wrote:
CAMANISHPARMAR wrote:
The "point-slope" form of the equation of a straight line is:
y2 − y1 = m(x2 − x1)
Therefore m = \(\frac{(y2 − y1)}{(x2 − x1)}\)
We have to determine the coordinate of the point where this line intercepts x-axis but the coordinate of y at this point is equal to 0.
Hence if we plug in the values of the two points as provided in the question stem & equate in the aforesaid formula we get the value of x intercept as -3
Hence option B is the correct answer.
Hi Manish, Please check the equation of line in 2 point form .
Only the slope formula is required which is correct!
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_________________ Manish
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If line k passes through the points (48, 33) and (31, 22),
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10 Jul 2018, 10:33
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GMATPrepNow wrote:
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?
A) -25 10/11 B) -3 C) -1 16/17 D) 1 16/17 E) 25 10/11
*kudos for all correct solutions
Shorter approaches are listed above. If those methods are unfamiliar and you know the slope-intercept equation of a line, the latter can be used without shortcuts to find the x-intercept.
Given: the line passes through points (48, 33) and (31, 22)
• Slope-intercept equation of a line: \(y=mx+b\)
\(m\) = slope and \(b\) = y-intercept. Find \(m\) and plug it into equation. Then find \(b\) and plug in. From that point find x-intercept.
*When clearing the fraction, do not do the multiplication. Number sense: 11 can be factored out . . . Or that fact will be clear when 11 in one term is next to 22 in the other on LHS. If numbers seem awkward and/or huge, often it is smarter to leave them factored.
Re: If line k passes through the points (48, 33) and (31, 22),
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14 Jul 2018, 18:31
GMATPrepNow wrote:
If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?
A) -25 10/11 B) -3 C) -1 16/17 D) 1 16/17 E) 25 10/11
We can let the x-intercept be a. Thus the coordinates of the x-intercept will be (a, 0). Since the x-intercept is on line k, the slope measured between the x-intercept and one of the two given points equals the slope measured between the two given points. Using the slope formula, we have:
(0 - 33)/(a - 48) = (22 - 33)/(31 - 48)
-33/(a - 48) = -11/(-17)
3/(a - 48) = 1/(-17)
a - 48 = -51
a = -3
Answer: B
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