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

Question

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

Nikhil · Accepted Answer

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

yoannnesme · Answer

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

PKN · Answer

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)

CAMANISHPARMAR · Answer

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.

PKN · Answer

Hi Manish,
Please check the equation of line in 2 point form .

CAMANISHPARMAR · Answer

Only the slope formula is required which is correct!

generis · Answer

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.

BrentGMATPrepNow · Answer

If we sketch the two given points, we can quickly see that   the slope (aka rise/run) of the line = 11/17  
 https://i.imgur.com/jJtP4PZ.png

So, we can use this information to plot another point on the line... 
 https://i.imgur.com/pfA3jL1.png

And another point... 
 https://i.imgur.com/tJq3B0j.png 
..at which point, we can see that the x-intercept is   -3

Answer: B

Cheers,
Brent

JeffTargetTestPrep · Answer

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

Kinshook · Answer

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

bumpbot · Answer

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

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