In a rectangular coordinate system, straight line k passes

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Tue Mar 03, 2020 6:33 am

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In a rectangular coordinate system, straight line k passes through points (0, 0) and (3, 2). Which of the following are coordinates of a point on k ?

A. (9, 4)
B. (4, 9)
C. (–4, 6)
D. (–6, –9)
E. (–6, –4)

Answer: E
Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Tue Mar 03, 2020 6:33 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

Re: In a rectangular coordinate system, straight line k passes

by Jay@ManhattanReview » Tue Mar 03, 2020 10:32 pm

BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:33 am
In a rectangular coordinate system, straight line k passes through points (0, 0) and (3, 2). Which of the following are coordinates of a point on k ?

A. (9, 4)
B. (4, 9)
C. (–4, 6)
D. (–6, –9)
E. (–6, –4)

Answer: E
Source: Official Guide

Slope of the like k = (2 – 0)/(3 – 0) = 2/3;

Let's see which point if it lies on line k also has the slope 2/3.

A. (9, 4): Slope of the line = (4 – 0)/(9 – 0) = 4/9 ≠ 2/3. Not the correct answer.

B. (4, 9): Slope of the line = (9 – 0)/(4 – 0) = 9/4 ≠ 2/3. Not the correct answer.

C. (–4, 6): Slope of the line = (6 – 0)/(–4 – 0) = –3/2 ≠ 2/3. Not the correct answer.

D. (–6, –9): Slope of the line = (–9 – 0)/(–6 – 0) = 3/2 ≠ 2/3. Not the correct answer.

E. (–6, –4): Slope of the line = (–4 – 0)/(–6 – 0) = 2/3 = 2/3. The correct answer.

The correct answer: E

Hope this helps!

-Jay
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: In a rectangular coordinate system, straight line k passes

by Brent@GMATPrepNow » Wed Mar 04, 2020 6:22 am

BTGModeratorVI wrote: ↑
Tue Mar 03, 2020 6:33 am
In a rectangular coordinate system, straight line k passes through points (0, 0) and (3, 2). Which of the following are coordinates of a point on k ?

A. (9, 4)
B. (4, 9)
C. (–4, 6)
D. (–6, –9)
E. (–6, –4)

Answer: E
Source: Official Guide

Key concept: If a point lies ON a line, then the coordinates of that point must SATISFY the equation of that line.

So, let's first find the equation of the line.
Slope = (y2 - y1)/(x2 - x1) = (2 - 0)/(3 - 0) = 2/3
The y-intercept = 0

So, the equation of the line, in slope y-intercept form, is: y = (2/3)x + 0 or just y = 2x/3

Now check each answer choice to see which coordinates satisfy the equation y = 2x/3

A. (9, 4)
Plug values into y = 2x/3 to get: 4 = (2)(9)/3
Simplify: 9 = 6
Doesn't work.
ELIMINATE A

B. (4, 9)
Plug values into y = 2x/3 to get: 9 = (2)(4)/3
Simplify: 9 = 8/3
Doesn't work.
ELIMINATE B

C. (–4, 6)
Plug values into y = 2x/3 to get: 6 = (2)(-4)/3
Simplify: 6 = -8/3
Doesn't work.
ELIMINATE C

D. (–6, –9)
Plug values into y = 2x/3 to get: -9 = (2)(-6)/3
Simplify: -9 = -4
Doesn't work.
ELIMINATE D

E. (–6, –4)
Plug values into y = 2x/3 to get: -6 = (2)(-4)/3
Simplify: -6 = -6
WORKS!!

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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