In the coordinate plane, line k passes through the origin and has slop

Question

In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x + y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

KarishmaB · Accepted Answer

In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

To find the line k, knowing a point through which it passes and the line's slope is sufficient.
Since it passes through origin and has slope 2, this is what it will look like:

Attachment:

Ques6.jpg [ 4.9 KiB | Viewed 74322 times ]

What is the meaning of slope? It means for every increase of 1 unit in x coordinate, y coordinate increases by 2 units. When x coordinate increases by 3 units (from the point (0,0)), y coordinate increases by 6 units. Hence the line passes through (3, 6). y must be 6.
When y coordinate increases by 4 units (from (0,0)), x coordinate must have increased by 2 units. The line must pass through (2, 4). x must be 2.
x+y = 2+6 = 8

Bunuel · Answer

In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Any line which passes through the origin has a form of  y=mx , since  m=2  (the slope of a line), then we have that the equation of our line is  y=2x . Now, if we substitute the coordinates of two points we'll get:

For point (3,y) -->  y=2*3=6 ;

For point (x,4) -->  4=2x  -->  x=2 ;

x+y=8 .
 
Answer: C.

fluke · Answer

Sol:
y=mx+c
m=Slope=2
c=intersection on y-axis=0
y=2x

The line passes through (3,y)
y=2*3=6

The line also passes through (x,4)
4=2*x;
x=2;

x+y=2+6=8

Ans: "C"

arnoorichenna · Answer

I think we have to go with general equation of line with two points.

y-y1/y2-y1 = x-x1/x2-x1

And substituting the values:

y-4 = 2(x-x1) => x1 =2 (as (0,0) is on the line).
4-y1=2(x-3) => y1= 6 (as (0,0) is on the line).

x+y = 8; Ans:C.

Spidy001 · Answer

x and y in those points (x,4) and y in (3,y) can be confusing .

you ran into this situation because you are trying to solve two equations y = 2x and 2x+y=10.

Thats not correct x and y in 2x+y = 10 refer to x in (x,4) and y in (3,y) and belong to two different points

where as y=2x is the generic equation . here x and y belong to same point.

to avoid confusion i would say you can replace the points as (3,p) and (q,4) and rephrase the question as p+q=?

equation of the line passing through origin and slope 2 => y = 2x

then you can compare slopes

slope of (3,p) and (0,0) = 2 => p/3 = 2 => p=6
slope of (q,4) and (0,0) = 2 => 4/q = 2 => q = 2

=> p+q = 8

thisiszico2006 · Answer

Points (3,y) and origin lies on the same line and have a slope of 2.
So (y-0)/(3-0)=2 or y=6

Points (x,4) and origin lies on the same line and have a slope of 2.
So (4-0)/(x-0)=2 or x=2

So x+y=8 ..

Answer choice (C)

Ashamock · Answer

I got this wrong and I cant figure what is wrong with my approach
(y2-y1)/(x2-x1)=m (slope)
so we have 2 points 
x,4 and 3,y
so we get the eq 
(y-4)/(3-x)=2.

simplifying this we get : 
y= 10-2x

so I get the value of y=4 and x=3 and hence the sum 7.

Why is this wrong?

Bunuel · Answer

Welcome to GMAT Club. Below is an answer to your question: There are infinitely many values of x and y possible to satisfy y=10-2x. For any value of x there exist some y for which y=10-2x holds true (and vise versa). For example: x=1, y=8 or x=2, y=6, or x=0.5, y=9, ... Also notice that you won't be able to find the value of x+y without one more piece of information given in the stem, namely information saying that line k passes through the origin. Check Coordinate Geometry chapter of Math Book for more on this subject: https://gmatclub.com/forum/math-coordina ... 87652.html Hope it helps.

KarishmaB · Answer

Let me point out one thing I noticed: How did you get y = 4 and x = 3?
The equation you get is y= 10-2x. Mind you, here y = y2 and x = x1 i.e. they are y and x co-ordinates of different points.
y = 10 - 2x can give you the value of y + 2x i.e. equal to 10 but how do you get the value of (y+x)?
You can go from here and find the answer if you consider the info that the line passes through the center. Say, the 2 points on the line that you are considering are (0, 0) and (x, 4)
(y2-y1)/(x2-x1)=m
(4 - 0)/(x - 0) = 2
x = 2

Now you can plug x = 2 in y = 10 - 2x to get y = 6
Their sum 2+6 = 8
Hope you understand that these x and y stand for particular values.

AKG1593 · Answer

Option C.
Origin=(0,0)
Let P1=(3,y)
Equation for line=>y-0=2(3-0)
y=6
Similarly,4-0=2(x-0)
x=2
x+y=8

beatthegmat05 · Answer

Slope of a line which passes through two point (x1,y1) and (x2,y2) is given by-
m=(y2-y1)/(x2-x1)

here m = 2 
Here one point is Origin (0,0)
substituting the given values -
2 =(y-0)/(3-0)
y= 6

Similarly, for other point 
2 =(4-0)/(x-0)
x =2

So x+y = 8

So correct answer is option C

Lucky2783 · Answer

Similar question : in-the-coordinate-plane-points-x-1-and-10-y-163337.html

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved with a "brute force" approach, as long as you understand the Graphing vocabulary involved.

We're told that a line passes through the ORIGIN (meaning point 0,0) and has a SLOPE of 2 (meaning the Y-coordinate increases by 2 every time the X-coordiinate increases by 1).

Thus, we can list the first several points (starting at the Origin) without too much trouble:
(0, 0)
(1, 2)
(2, 4)
(3, 6)
(4, 8)
(5, 10)
Etc.

We're told that (3, Y) and (X, 4) are on this line. We're asked for the value of X+Y....

From the list (above), we can see that Y = 6 and that X = 2, so X+Y = 2+6 = 8

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

kanav06 · Answer

I'm stumped!

what is wrong in the approach below?

y= 2x+c (we know that c=0). Thus,
y=2x........equation 1

next, 
(4-y)/(x-3)= 2
Thus, 10= 2x+y....equation 2

From equation 1 & equation 2, I found x= 5/2 & y= 5.
Thus x+y= 7.5

I'm not understanding what is wrong in this process!

KarishmaB · Answer

y = 2x is the equation of the line - fine.

But these two - (3,y) and (x,4) are points. Here y and x are specific co-ordinate points.

Think of them instead as points (3, a) and (b, 4). You need to find a + b.
You will get 10 = 2a + b by equating it to slope but how will you solve for a + b?

The equation of the line is y = 2x
So a = 2*3 = 6
Also, 4 = 2*b
b = 2

So a + b = 6 + 2 = 8

nishatfarhat87 · Answer

Hi Bunuel,

Why is the answer wrong if I do the question in the following way:

y=mx
y=2x
x+y = x+2x = 3x
Now from values given, 4 = 2x
x = 2
x+y = 3*2 = 6

EMPOWERgmatRichC · Answer

Hi nishatfarhat87,

In your work, you're confusing the VARIABLES X and Y with the X and Y co-ordinates on the line. Try doing your math again, but use these variables instead...

Y = 2X

(3, B) and (A, 4) are on the line. What is the value of A+B?

GMAT assassins aren't born, they're made,
Rich

JeffTargetTestPrep · Answer

We are given that line k passes through the origin (or the point (0,0)) and has a slope of 2. Since slope = (change in y)/(change in x), we can create the following equation using the coordinates (0,0) and (3,y):

2 = (y - 0)/(3 - 0)

2 = y/3

y = 6

We can use the slope equation again, this time using the coordinates (0,0) and (x,4):

2 = (4 - 0)/(x - 0)

2 = 4/x

2x = 4

x = 2

Thus, x + y = 6 + 2 = 8.

Answer: C

BrentGMATPrepNow · Answer

It often helps to write equations for lines in the form  y = mx + b  (this is called slope y-intercept form), where m = the slope of the line, and b = the y-intercept of the line.

The question tells us that the line has slope 2. So,  m = 2 
The question also tells us that the line passes through the origin (0,0). So, the y-intercept is 0, which means b = 0
So, the equation of the line is y = 2x + 0, or just  y = 2x

If the point (3,y) is on the line, then its coordinates must satisfy the equation  y = 2x 
So, plug x=3 and y=y into the equation to get y = (2)(3) =  6

If the point (x,4) is on the line, then its coordinates must satisfy the equation  y = 2x 
So, plug x=x and y=4 into the equation to get 4 = 2x, which means x =  2

So, x + y =  2  +  6  
= 8 
= C

Cheers,
Brent

In the coordinate plane, line k passes through the origin and has slop

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In the coordinate plane, line k passes through the origin and has slop

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