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

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If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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09 Jul 2018, 06:22
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Difficulty:

55% (hard)

Question Stats:

59% (01:53) correct 41% (02:49) wrong based on 78 sessions

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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

*kudos for all correct solutions

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If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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09 Jul 2018, 06:56
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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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##### General Discussion
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Joined: 17 May 2018
Posts: 38
Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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09 Jul 2018, 06:50
2
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).

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If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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09 Jul 2018, 07:35
1
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]

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Updated on: 09 Jul 2018, 08:26
1
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.
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Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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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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Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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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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If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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10 Jul 2018, 10:33
2
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.

$$0=\frac{11}{17}x+\frac{33}{17}$$
$$0=11x+33$$
$$-33=11x$$
$$-\frac{33}{11}=x$$
$$-3=x$$

*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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Joined: 11 Sep 2015
Posts: 3122
Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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11 Jul 2018, 07:02
1
Top Contributor
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

Cheers,
Brent
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Re: If line k passes through the points (48, 33) and (31, 22),  [#permalink]

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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

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Re: If line k passes through the points (48, 33) and (31, 22), &nbs [#permalink] 14 Jul 2018, 18:31
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