A line in the xy-plane passes through the origin and has a slope of 1/

Question

A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?

A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)

sashiim20 · Accepted Answer

Line passes through origin. Hence one point line passes through would be (0,0). Let  (x1,y1) = (0,0)

Given Slope  = \frac{1}{7}

Slope of line  = \frac{y2 - y1}{x2 - x1}

\frac{1}{7} = \frac{y2 - 0}{x2 - 0}

\frac{y2}{x2} = \frac{1}{7}

Therefore point  (x2,y2) = (7,1)

From the options, point that lies on line  = (14,2)  . Answer (D) ...

BrentGMATPrepNow · Answer

Let's write the equation of the line in  slope y-intercept form  y = mx + b, where m = the slope and b = the y-intercept.

So, m = 1/7
And, since the line passes through the origin (0,0), we know that b (the y-intercept) = 0
So, the equation of the line is: y = (1/7)x + 0
Or just y = (1/7)x

So, all points (x, y) ON the line will satisfy the equation y = (1/7)x
Let's check the answer choices.

A) (0, 7) plug x = 0 and y = 7 into the equation of the line to get: 7 = (1/7)(0) Doesn't work. So, (0,7) is NOT on the line. 
B) (1, 7) plug x = 1 and y = 7 into the equation of the line to get: 7 = (1/7)(1) Doesn't work. So, (1,7) is NOT on the line. 
C) (7, 7) plug x = 7 and y = 7 into the equation of the line to get: 7 = (1/7)(7) Doesn't work. So, (7,7) is NOT on the line. 
D) (14, 2) plug x = 14 and y = 2 into the equation of the line to get: 2 = (1/7)(14) This WORKS. So, (2,14) IS on the line.

Answer: D

arvind910619 · Answer

Answer is D
Slope intercept form of the line y=mx+c
Line passes through origin thus we have c=0
y=mx
m=1/7
7y=x only D satisfies the equation.

generis · Answer

Should you not remember the slope intercept formula (y = mx + b), or any other method, you do know two things:

1) The line passes through (0,0), so that is a point on the line; and

2) The slope is 1/7, rise/run, which means from any point on the line, such as (0,0), you can count one up and seven over to the right to find another point.

Do that twice, starting from (0,0). The first point you'll "land on" is (7,1). Then again count one up and seven over from that point, and you land on (14,2).

Answer D

tapabrata · Answer

An important formula.

If we know the slope of a line and one point (x1,y1) that it passes through, then the equation of the line is

y-y1=m(x-x1)

We know the line passes through origin (0,0).
Putting x1=0 and y1=0 we get the equation as

y=mx => y=(1/7)x

so for any point on the line, the y-coordinate will be 1/7 times the x-coordinate.

Checking the options, only D satisfies it (x-coordinate =14, y-coordinate=1/7 times 14 =2)

Answer D

ydmuley · Answer

Slope = m = 1/7

As the line passes through the origin, the y intercept is ZERO, which means b = 0

we know, y = mx+b

y = 1/7.x+0

or x/y = 7

Now, lets quickly check the options which satisfy this equation:

A) (0, 7) - Nope, x/y != 7
B) (1, 7) - Nope, x/y != 7
C) (7, 7) - Nope, x/y != 7
  D) (14, 2) - Yes - x/y = 7  
E) (7, 14) - Nope, x/y != 7

Hence, Answer is D

brainwired · Answer

y=mx+c
The line passes through (0,0) with slope=1/7. Plug in above equation 
c=0

So y=mx
m=1/7 (given)
7y=x

Find the answer choice where your y is 7 times your x

Answer D.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A line in the xy-plane passes through the origin and has a slope of 1/

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A line in the xy-plane passes through the origin and has a slope of 1/

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards