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In the xycoordinate plane, line l passes through the point (3, 0).
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12 Nov 2014, 10:09
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Re: In the xycoordinate plane, line l passes through the point (3, 0).
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12 Nov 2014, 10:19
In the xycoordinate plane, line l passes through the point (3, 0). Does line l pass through the point (0, \frac{3}{4})?
(1) The slope of line l is \frac{1}{4}.
(2) Line l passes through the point (5, 2).
1). With this slope, the line increases height by 1/4 for each movement towards a higher X value. 3 to 0 is 3 movements. 3*1/4 = 3/4. sufficient.
2) delta y over delta x is slope. (20) / (5(3)) = 2/8 = 1/4 = same as 1) = sufficient.
Answer is D?



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Re: In the xycoordinate plane, line l passes through the point (3, 0).
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12 Nov 2014, 10:49
statement 1: sufficient no need for calculations, since we are given a starting point, we can use the slope to draw the line and see if it passes through (0, 3/4). statement 2: sufficient we now have 2 points on of the line and with this we can figure out the slope and figure out if it passes through (0, 3/4). again, no need for calculations Answer D!



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Re: In the xycoordinate plane, line l passes through the point (3, 0).
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12 Nov 2014, 20:16
Statement 1: The slope of line l is 1/4 .
We can find out the equation of the line , 1/4(x+3)=y, and therefore by replacing x by 0 and y by 3/4, we know that the line passes through the point. Sufficient
Statement 2: Line l passes through the point (5, 2).
Similarly, we can find the equation of the line and then equate it with (0,3/4). Sufficient
D) should be the answer



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Re: In the xycoordinate plane, line l passes through the point (3, 0).
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13 Nov 2014, 09:14
Bunuel wrote: Tough and Tricky questions: Coordinate Geometry. In the xycoordinate plane, line \(l\) passes through the point \((3, 0)\). Does line \(l\) pass through the point \((0, \frac{3}{4})\)? (1) The slope of line \(l\) is \(\frac{1}{4}\). (2) Line \(l\) passes through the point \((5, 2)\). Kudos for a correct solution. Official Solution: We start by writing the equation of line \(l\) in slopeintercept form: \(y = mx + b\), where \(m\) is the slope and \(b\) is the yintercept. We are asked if the line passes through \((0, \frac{3}{4})\). Recall that the yintercept is the point where the line crosses the yaxis, or, equivalently, the point on the line where \(x = 0\). Therefore, \((0, \frac{3}{4})\) is a potential yintercept. We must determine if, in the equation of line \(l\), \(b\) is equal to \(\frac{3}{4}\). Statement 1 gives us the slope of the line, which we can plug into the equation: \(y = \frac{1}{4}x + b\). In the prompt, we are also given a point on the line: \((3, 0)\). Plugging in this point makes the equation: \(0 = \frac{1}{4}(3) + b\). This simplifies to \(b = \frac{3}{4}\), and so line \(l\) does pass through the point \((0, \frac{3}{4})\). Statement 1 is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice must be A or D. Statement 2 tells us that line \(l\) passes through the point \((5, 2)\). Along with the xintercept, \((3, 0)\), we now have two points on the line, which is enough to find the slope. As we saw with statement 1, knowing the slope and one point on the line is enough to find the yintercept. Since we can find the yintercept, we know that we can find the answer to the question, even though we do not yet know whether the answer is yes or no. Therefore, statement 2 is also sufficient to answer the question. Answer choice D is correct. Recall that when we are given two points, we can always find the slope: \(slope = \frac{\text{rise}}{\text{run}} = \frac{y_2  y_1}{x_2  x_1}\). In this case, since our two points are \((3, 0)\) and \((5, 2)\), \(m = \frac{0  2}{3  5} = \frac{2}{8} = \frac{1}{4}\). We saw in examining statement 1 that if line \(l\) has slope equal to \(\frac{1}{4}\) and passes through the point \((3, 0)\), it will have a yintercept of \(\frac{3}{4}\), as desired. Answer: D.
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Re: In the xycoordinate plane, line l passes through the point (3, 0).
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16 Jul 2018, 11:27
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Re: In the xycoordinate plane, line l passes through the point (3, 0). &nbs
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