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If line k passes through the points (48, 33) and (31, 22),

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BrentGMATPrepNow
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If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   09 Jul 2018, 07:22
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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

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If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   09 Jul 2018, 07:56
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Since y-coordinate is 0 at which the line intercepts x-axis. Let (a,0) be the point where the the line meets x-axis.

Since (48,33), (31,22), (a,0) all lie on the same line, the slope calculated using any two of these points is equal

=> \(\frac{(33-22)}{(48-31)} = \frac{(22-0)}{(31-a)}\)

=> \(\frac{11}{17} = \frac{22}{(31-a)}\)

=> \(11 * (31-a) = 22 * 17\)

=> \(31 - a = 34\)

=> \(a = -3\)

Hence option B
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Re: If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   09 Jul 2018, 07:50
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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), [#permalink] New post   09 Jul 2018, 08:35
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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), [#permalink] New post   Updated on: 09 Jul 2018, 09:26
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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.

Originally posted by CAMANISHPARMAR on 09 Jul 2018, 09:06.
Last edited by CAMANISHPARMAR on 09 Jul 2018, 09:26, edited 1 time in total.
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Re: If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   09 Jul 2018, 09:17
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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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Re: If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   09 Jul 2018, 09:25
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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If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   10 Jul 2018, 11:33
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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.

• Slope = \(\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{33-22}{48-31}=\frac{11}{17}\)

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*:
\((17*22)=(11*31)+17b\)
\((17*2*11) - (11*31)=17b\)
\(11(34-31)=17b\)
\(33=17b\)
\(b=\frac{33}{17}\)

Equation with \(b\) plugged in: \(y=\frac{11}{17}x+\frac{33}{17}\)

• x-intercept? 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), [#permalink] New post   11 Jul 2018, 08:02
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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


If we sketch the two given points, we can quickly see that the slope (aka rise/run) of the line = 11/17


So, we can use this information to plot another point on the line...


And another point...

..at which point, we can see that the x-intercept is -3

Answer: B

Cheers,
Brent
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Re: If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   14 Jul 2018, 19:31
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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


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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Re: If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   04 Jan 2023, 22:59
Asked: If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

Let the equation of the line be: -
x/a + y/b = 1
where a is the x-intercept
and b is the y-intercept

Since Point (48,33) passes through line k, it must satisfy its equation.
48/a + 33/b = 1

Since Point (31,22) passes through line k, it must satisfy its equation.
31/a + 22/b = 1

17/a + 11/b = 0
17/a = - 11/b
b = -11a/17

31/a -22*17/11a = 1
31/a - 34a = 1
a = -3

IMO B
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Re: If line k passes through the points (48, 33) and (31, 22), [#permalink] New post   15 Feb 2024, 02:31
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Re: If line k passes through the points (48, 33) and (31, 22), [#permalink]
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