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# In the xy-coordinate plane, line l passes through the point (-3, 0).

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Math Expert
Joined: 02 Sep 2009
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In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

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12 Nov 2014, 10:09
1
5
00:00

Difficulty:

15% (low)

Question Stats:

76% (00:49) correct 24% (00:45) wrong based on 156 sessions

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Tough and Tricky questions: Coordinate Geometry.

In the xy-coordinate 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.

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Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

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12 Nov 2014, 10:19
1
In the xy-coordinate 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. (2-0) / (5-(-3)) = 2/8 = 1/4 = same as 1) = sufficient.

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Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

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12 Nov 2014, 10:49
1
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

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Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

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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

Math Expert
Joined: 02 Sep 2009
Posts: 46191
Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

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13 Nov 2014, 09:14
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

In the xy-coordinate 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 slope-intercept form: $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. We are asked if the line passes through $$(0, \frac{3}{4})$$. Recall that the y-intercept is the point where the line crosses the y-axis, or, equivalently, the point on the line where $$x = 0$$. Therefore, $$(0, \frac{3}{4})$$ is a potential y-intercept. 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 x-intercept, $$(-3, 0)$$, 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 y-intercept. Since we can find the y-intercept, 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.

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 y-intercept of $$\frac{3}{4}$$, as desired.

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Re: In the xy-coordinate plane, line l passes through the point (-3, 0). [#permalink]

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15 May 2017, 19:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the xy-coordinate plane, line l passes through the point (-3, 0).   [#permalink] 15 May 2017, 19:31
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