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A line has a slope of 3/4 and intersects the point (12, 39). At whic
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Updated on: 12 Dec 2015, 07:21
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A line has a slope of 3/4 and intersects the point (12, 39). At which point does this line intersect the xaxis? A. (40,0) B. (30,0) C. (0,40) D. (40,30) E. (0,30) My solutuion was:
y=3/4x+b 39=3/4(12)+b 39=9+b b=30
But he asks for xaxis, I´m confused here...
Please, send me your solutions.
thanks Solution by the book: (40,0)
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Originally posted by bitenca on 12 Dec 2015, 07:17.
Last edited by ENGRTOMBA2018 on 12 Dec 2015, 07:21, edited 1 time in total.
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Re: A line has a slope of 3/4 and intersects the point (12, 39). At whic
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12 Dec 2015, 07:26
bitenca wrote: A line has a slope of 3/4 and intersects the point (12, 39). At which point does this line intersect the xaxis? A. (40,0) B. (30,0) C. (0,40) D. (40,30) E. (0,30) My solutuion was:
y=3/4x+b 39=3/4(12)+b 39=9+b b=30
But he asks for xaxis, I´m confused here...
Please, send me your solutions.
thanks Solution by the book: (40,0) I have modified your original post. As for your question, Assume that the equation of the line is y=mx+c, where m and c are the slope and yintercept. You are also given that the line crosses the point (12,39), this means that this point will also lie on the line above. Thus you get 39=m*(12)+c , with m=3/4 as the slope is given to be 3/4. After substituting the above values, you get c = 30. Thus the equation of the line is y=0.75*x30 and the point where it will intersect the xaxis will be with y coordinate = 0. Put y=0 in the above equation of the line and you will get, x=40. Thus, the point of intersection is (40,0). A is the correct answer.



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Re: A line has a slope of 3/4 and intersects the point (12, 39). At whic
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12 Dec 2015, 12:23
Engr2012 wrote: bitenca wrote: A line has a slope of 3/4 and intersects the point (12, 39). At which point does this line intersect the xaxis? A. (40,0) B. (30,0) C. (0,40) D. (40,30) E. (0,30) My solutuion was:
y=3/4x+b 39=3/4(12)+b 39=9+b b=30
But he asks for xaxis, I´m confused here...
Please, send me your solutions.
thanks Solution by the book: (40,0) I have modified your original post. As for your question, Assume that the equation of the line is y=mx+c, where m and c are the slope and yintercept. You are also given that the line crosses the point (12,39), this means that this point will also lie on the line above. Thus you get 39=m*(12)+c , with m=3/4 as the slope is given to be 3/4. After substituting the above values, you get c = 30. Thus the equation of the line is y=0.75*x30 and the point where it will intersect the xaxis will be with y coordinate = 0. Put y=0 in the above equation of the line and you will get, x=40. Thus, the point of intersection is (40,0). A is the correct answer. Ohh.. Now I see, thank you very much!! Eddie



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A line has a slope of 3/4 and intersects the point (12, 39). At whic
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12 Dec 2015, 12:32
bitenca wrote: A line has a slope of 3/4 and intersects the point (12, 39). At which point does this line intersect the xaxis? A. (40,0) B. (30,0) C. (0,40) D. (40,30) E. (0,30) My solutuion was:
y=3/4x+b 39=3/4(12)+b 39=9+b b=30
But he asks for xaxis, I´m confused here...
Please, send me your solutions.
thanks Solution by the book: (40,0) One last point to make: Even if we aren't sure how to actually answer the question, we can still recognize that for any point on the xaxis, the ycoordinate will equal 0. This one fact allows us to ELIMINATE answer choices C, D and E, leaving us with a 50% chance of guessing the correct answer. Here's a free video about x and yintercepts on the GMAT  http://www.gmatprepnow.com/module/gmat ... /video/996Cheers, Brent
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Re: A line has a slope of 3/4 and intersects the point (12, 39). At whic
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14 Dec 2015, 17:01
Hi bitenca, This question can be solved in a couple of different ways. If you're comfortable with the 'concept' of 'slope', then you can answer this question with just a bit of arithmetic. We're given some information about a line: 1) The line has a slope of 3/4 2) The line intersects the point (12,39) We're asked at which point the line will intersect the Xaxis. Since THAT coordinate will be (X, 0), we can use the slope to our advantage and 'count up' to that point: With a slope of 3/4, we know that the line will "go up 3 points and go forward 4 points", meaning that the first few coordinates would be... (12,39) (8, 36) (4, 33) (0, 30) Etc. We can continue to 'count up' from here OR do a bit of algebra: From the original coordinate, we know that we have to increase the '39' to a '0' in increments of 3. That will clearly take 13 increments (since 13x3 = 39). Those same 13 increments would 'add 4' each time to the original X coordinate, turning '12' into.....12 + (13x4) = 40. Thus, the answer is (40,0). Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: A line has a slope of 3/4 and intersects the point (12, 39). At whic
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30 Jul 2016, 02:51
The equation of the slope is (y2y1)/(x2x1). Here we have (y2+39)/(x2+12)=(3/4) ==> 4y +156=3x+36 . We need to find xinterscetion i.e the point where y=0 Hence we have 3x=120 and x=40 Point of xintersection is (40,0) Answer A
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Re: A line has a slope of 3/4 and intersects the point (12, 39). At whic
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30 Jul 2016, 05:11
> Equation of line with slope m and passing through (x1,y1) = (yy1)=m(xx1) So here m=3/4 and (x1,y1)=(12,39). So equation of line: (y+39)=3/4(x+12) ==> (y+39)=(3/4x+9) Now point where this line cuts xaxis is where y=0. So equation becomes: 0+39=3/4x+9 Therefore, x=40 (when y=0)
Answer(x,y)=(40,0) >>>> correct answer A



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Re: A line has a slope of 3/4 and intersects the point (12, 39). At whic
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30 Dec 2017, 01:14
Since we are looking for point on x axis, y coordinate should be zero, Thus we can eliminate option C, D, ELooking at option A40,0 slope = \(\frac{change in y}{change in x}\)= \(\frac{y_2y_1}{x_2x_1}\) ie. slope = \(\frac{390}{1240}\)=\(\frac{3}{4}\) thus option A is answer
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Re: A line has a slope of 3/4 and intersects the point (12, 39). At whic
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10 Aug 2018, 01:21
One can solve these type of questions easily if he/she knows who to convert given points into to slope equation. For example, the author gives two points (x,y) (x1,y1), and requires to turn these into y=mx+k form. Here is a great post bu Bunuel , check it out! https://gmatclub.com/forum/mathcoordin ... ml#p659245For this particular problem, the author gives us the slope of the equation, as well as one coordinate, such as slope= 3/4 and the coordinate, is (12,39). \(\frac{y(39)}{x(12)}\) =\(\frac{3}{4}\) 4(y+39)=3(x+12), so y=3x/430. To the the x intercept, we should plug in 0 for the y, and find out the coordinate, (40,0).
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