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If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 07:22
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If line k passes through the points (48, 33) and (31, 22), what is the xintercept of line k? A) 25 10/11B) 3 C) 1 16/17 D) 1 16/17E) 25 10/11*kudos for all correct solutions
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If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 07:56
Since ycoordinate is 0 at which the line intercepts xaxis. Let (a,0) be the point where the the line meets xaxis. Since (48,33), (31,22), (a,0) all lie on the same line, the slope calculated using any two of these points is equal => \(\frac{(3322)}{(4831)} = \frac{(220)}{(31a)}\) => \(\frac{11}{17} = \frac{22}{(31a)}\) => \(11 * (31a) = 22 * 17\) => \(31  a = 34\) => \(a = 3\) Hence option B
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Re: If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 07:50
If line passes through (31,22) and (48,33), it means that for every increase of 17 of x (4831), y will increase by 11 (3322). 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: (3117, 2211) which is (14,11) and (1417,1111) 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, 08:35
GMATPrepNow wrote: If line k passes through the points (48, 33) and (31, 22), what is the xintercept 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: y33=m(x48)where m=11/17 (General form of equation of line passing through two points (x1,y1) and (x2,y2): yy1=m(xx1)) and m=slope=(y2y1)/(x2x1) At x intercept ,y=0. So,we have 33=(11/17)(x48) Or, x48=51 Or, x=51+48=3 (please note this is the xintecept 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, 09:26
m (slope) = \(\frac{(y2 − y1)}{(x2 − x1)}\) We have to determine the coordinate of the point where this line intercepts xaxis 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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Re: If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 09:17
CAMANISHPARMAR wrote: The "pointslope" 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 xaxis 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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Re: If line k passes through the points (48, 33) and (31, 22),
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09 Jul 2018, 09:25
PKN wrote: CAMANISHPARMAR wrote: The "pointslope" 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 xaxis 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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If line k passes through the points (48, 33) and (31, 22),
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10 Jul 2018, 11:33
GMATPrepNow wrote: If line k passes through the points (48, 33) and (31, 22), what is the xintercept 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 slopeintercept equation of a line, the latter can be used without shortcuts to find the xintercept. Given: the line passes through points (48, 33) and (31, 22) • Slopeintercept equation of a line: \(y=mx+b\) \(m\) = slope and \(b\) = yintercept. Find \(m\) and plug it into equation. Then find \(b\) and plug in. From that point find xintercept. • Slope = \(\frac{rise}{run}=\frac{y_2y_1}{x_2x_1}=\frac{3322}{4831}=\frac{11}{17}\) Equation of the line with slope plugged in: \(y=\frac{11}{17}x+b\) • To find \(b\), plug in (x,y) values from one coordinate. Using (31,22)\(22=(\frac{11}{17}*31)+b\) Clear the fraction*: \((17*22)=(11*31)+17b\) \((17*2*11)  (11*31)=17b\) \(11(3431)=17b\) \(33=17b\) \(b=\frac{33}{17}\)Equation with \(b\) plugged in: \(y=\frac{11}{17}x+\frac{33}{17}\) • xintercept? Set y equal to 0 in the equation.\(0=\frac{11}{17}x+\frac{33}{17}\) \(0=11x+33\) \(33=11x\) \(\frac{33}{11}=x\) \(3=x\)Answer B *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.
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Re: If line k passes through the points (48, 33) and (31, 22),
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11 Jul 2018, 08:02
GMATPrepNow wrote: If line k passes through the points (48, 33) and (31, 22), what is the xintercept 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 If we sketch the two given points, we can quickly see that the slope (aka rise/run) of the line = 11/17So, we can use this information to plot another point on the line... And another point... ..at which point, we can see that the xintercept is 3Answer: B Cheers, Brent
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Re: If line k passes through the points (48, 33) and (31, 22),
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14 Jul 2018, 19:31
GMATPrepNow wrote: If line k passes through the points (48, 33) and (31, 22), what is the xintercept 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 xintercept be a. Thus the coordinates of the xintercept will be (a, 0). Since the xintercept is on line k, the slope measured between the xintercept 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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Re: If line k passes through the points (48, 33) and (31, 22), &nbs
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