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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.
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).
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)
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, E Looking at option A 40,0 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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71% (01:18) correct 
