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A line has a slope of 3/4 and intersects the point (-12, -39). At whic [#permalink]
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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 x-axis? 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 x-axis, 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.
Formatted the question
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Re: A line has a slope of 3/4 and intersects the point (-12, -39). At whic [#permalink]
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12 Dec 2015, 07:26
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bitenca wrote: A line has a slope of 3/4 and intersects the point (-12, -39). At which point does this line intersect the x-axis? 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 x-axis, 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 y-intercept. 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*x-30 and the point where it will intersect the x-axis 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 [#permalink]
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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 x-axis? 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 x-axis, 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 y-intercept. 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*x-30 and the point where it will intersect the x-axis 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 [#permalink]
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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 x-axis? 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 x-axis, 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 x-axis, the y-coordinate 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 y-intercepts 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 [#permalink]
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14 Dec 2015, 17:01
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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 X-axis. Since THAT co-ordinate 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 co-ordinates 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 co-ordinate, 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 co-ordinate, 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 [#permalink]
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30 Jul 2016, 02:51
The equation of the slope is (y2-y1)/(x2-x1). Here we have (y2+39)/(x2+12)=(3/4) ==> 4y +156=3x+36 . We need to find x-interscetion i.e the point where y=0 Hence we have 3x=120 and x=40 Point of x-intersection 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 [#permalink]
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30 Jul 2016, 05:11
--> Equation of line with slope m and passing through (x1,y1) = (y-y1)=m(x-x1)
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 x-axis 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 [#permalink]
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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 = \(\frac{change in y}{change in x}\)= \(\frac{y_2-y_1}{x_2-x_1}\) ie. slope = \(\frac{-39-0}{-12-40}\)=\(\frac{3}{4}\) 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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30 Dec 2017, 01:14
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