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M11-12

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Bunuel
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M11-12 [#permalink] New post   16 Sep 2014, 00:44
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If the line \(y = kx + b\) intersects the x-axis at \((2, 0)\) and the y-axis at \((0, 5)\), what is the value of \(\frac{k}{b}\)?

A. \(-\frac{5}{2}\)
B. \(-\frac{5}{4}\)
C. \(-\frac{1}{2}\)
D. \(\frac{2}{5}\)
E. \(\frac{4}{5}\)
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C
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Bunuel
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Re M11-12 [#permalink] New post   16 Sep 2014, 00:44
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Official Solution:

If the line \(y = kx + b\) intersects the x-axis at \((2, 0)\) and the y-axis at \((0, 5)\), what is the value of \(\frac{k}{b}\)?

A. \(-\frac{5}{2}\)
B. \(-\frac{5}{4}\)
C. \(-\frac{1}{2}\)
D. \(\frac{2}{5}\)
E. \(\frac{4}{5}\)


Substituting \((0, 5)\) for \((x, y)\) into \(y = kx + b\) gives us \(5 = 0 + b\), resulting in \(b = 5\).

Substituting \((2, 0)\) for \((x, y)\) into \(y = kx + b\) gives us \(0 = 2k + b\). Since we already know that \(b = 5\), then \(k = -\frac{5}{2}\).

Therefore, \(\frac{k}{b} = \frac{(-\frac{5}{2})}{5} = -\frac{1}{2}\).

Note that while Geometry is not tested on GMAT Focus, coordinate geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.


Answer: C
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Re: M11-12 [#permalink] New post   29 Jan 2016, 14:35
Alternate Solution :

Point 1 = (2,0)
Substituting for x and y in the first equation gives 0 = k(2) + b => 2k = -b => (k/b) = (-1/2)

IMO, we don't need the 2nd equation or the second point to solve this question.
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Re: M11-12 [#permalink] New post   23 Jun 2016, 06:58
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Note: This could have been actually a very interesting Data Sufficiency question! Something like this:

For the straight line y = kx + b, what is the value of (k/b)?
Statement 1: The line intersects x-axis at (2, 0)
Statement 2: The line intersects y-axis at (0, 5)

Anyway, the simple solution for this given question is:
We know that for a straight line y = mx + c (standard equation),
y-intercept = c;
x-intercept = - c/m;

Here the equation is y = kx + b;
Thus, y-intercept = b;
x-intercept = - b/k;

We are supposed to find (k/b). So let's ignore y-intercept. Let's focus on x-intercept.
- b/k = 2
So, b/k = - 2
So, k/b = - 1/2

Ans: C
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Bunuel
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Re: M11-12 [#permalink] New post   04 Feb 2024, 08:18
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M11-12 [#permalink]
04 Feb 2024, 08:18
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Bunuel
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