A straight line has a slope of 1/2 and a y-intercept of

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

A straight line has a slope of 1/2 and a y-intercept of

by VJesus12 » Tue Jun 05, 2018 1:45 am

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A straight line has a slope of 1/2 and a y-intercept of -2. On this line, what is the x-coordinate of the point whose y-coordinate is 10?

1. (8)
2. (12)
3. (13)
4. (16)
5. (24)

The OA is the option E.

How can I find the x-coordinate? Could anyone tell me how to find the equation of the line? Thanks for your help.

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Source: Beat The GMAT — Problem Solving | Tue Jun 05, 2018 1:45 am

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

by Brent@GMATPrepNow » Tue Jun 05, 2018 7:13 am

VJesus12 wrote:A straight line has a slope of 1/2 and a y-intercept of -2. On this line, what is the x-coordinate of the point whose y-coordinate is 10?

A. (8)
B. (12)
C. (13)
D. (16)
E. (24)

Given this information, we can write the equation for the line in slope y-intercept form, y = mx + b, where m = the slope and b = the y-intercept

We're told that the slope is 1/2 and the y-intercept is -2
So, the equation of the line is: y = (1/2)x + (-2)
Simplify to get: y = (1/2)x - 2

What is the x-coordinate of the point whose y-coordinate is 10?
In other words, what does x equal when y = 10?
Take the equation of the line, y = (1/2)x - 2 and replace y with 10 to get: 10 = (1/2)x - 2 [now solve for x]
Add 2 to both sides: 12 = (1/2)x
Solve, x = 24

So, when y = 10, x = 24

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jun 06, 2018 3:59 pm

VJesus12 wrote:A straight line has a slope of 1/2 and a y-intercept of -2. On this line, what is the x-coordinate of the point whose y-coordinate is 10?

1. (8)
2. (12)
3. (13)
4. (16)
5. (24)

We use the slope-intercept formula for a line: y = mx + b, where m = the slope of the line and b = the y-intercept of the line. Therefore, the equation of the line is:

y = (1/2)x - 2

So, if y = 10, then:

10 = x/2 - 2

12 = x/2

24 = x

Answer: E

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