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# In the xy-plane, line L has equation y=mx+b, where 1<m<5. If line L

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Math Revolution GMAT Instructor
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In the xy-plane, line L has equation y=mx+b, where 1<m<5. If line L  [#permalink]

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04 Jul 2018, 00:54
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45% (medium)

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67% (02:05) correct 33% (02:23) wrong based on 46 sessions

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[GMAT math practice question]

In the xy-plane, line L has equation $$y=mx+b$$, where $$1<m<5$$. If line L passes through (1,1), which of the following points also lies on line L?

A. (2, -1)
B. (2,0)
C. (2,1)
D. (2,2)
E. (2,3)

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7106 Re: In the xy-plane, line L has equation y=mx+b, where 1<m<5. If line L [#permalink] ### Show Tags 04 Jul 2018, 01:24 MathRevolution wrote: [GMAT math practice question] In the xy-plane, line L has equation $$y=mx+b$$, where $$1<m<5$$. If line L passes through (1,1), which of the following points also lies on line L? A. (2, -1) B. (2,0) C. (2,1) D. (2,2) E. (2,3) Use equation to solve.. $$y=mx+b............1=m+b........ b=1-m.$$ Since b is constant, y=mx+b=mx+1-m Now all choices contain x as 2, substitute y=2m+1-m=m+1 Now 1<m<5 ....... Add 1 to all 1+1<m+1<5+1......2<m+1<6 In all choices Only value given is 3 So ans (2,3) E _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Manager Joined: 19 Nov 2017 Posts: 174 Location: India Schools: ISB GMAT 1: 670 Q49 V32 GPA: 4 Re: In the xy-plane, line L has equation y=mx+b, where 1<m<5. If line L [#permalink] ### Show Tags 04 Jul 2018, 01:49 MathRevolution wrote: [GMAT math practice question] In the xy-plane, line L has equation $$y=mx+b$$, where $$1<m<5$$. If line L passes through (1,1), which of the following points also lies on line L? A. (2, -1) B. (2,0) C. (2,1) D. (2,2) E. (2,3) $$y=mx + b$$ 1 (1,1) is a point on the line Substitute $$X=1$$ and $$Y=1$$ We get $$m=-b$$ 2 Substitute 2 in 1 $$y=-bx+b$$ Options A, B, C can be eliminated because value of B will be less than 1 and this the value of M would not meet the criteria mentioned in the question. Options D and E would fit the criteria, however, Option D can be eliminated because if (2,2) is a point and (1,1) is a point on the line, then the slope, m, would be equal to 1. But $$1<m<5$$. Therefore, Option E. _________________ Regards, Vaibhav Sky is the limit. 800 is the limit. ~GMAC Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the xy-plane, line L has equation y=mx+b, where 1<m<5. If line L [#permalink] ### Show Tags 06 Jul 2018, 00:44 => When we plug in the values $$x = 1$$ and $$y = 1$$, we obtain $$1 = m + b$$ or $$b = 1 – m$$. All answer choices have x-coordinates of 2. Plugging 2 in for the variable $$x$$ yields $$y = 2m + b = 2m + 1 – m = m + 1.$$ Since $$1 < m < 5$$, we must have $$2 < m + 1 < 6$$ and $$2 < y < 6.$$ Thus, $$(2,3)$$ is the only point that can lie on the line. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: In the xy-plane, line L has equation y=mx+b, where 1<m<5. If line L &nbs [#permalink] 06 Jul 2018, 00:44
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