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In the coordinate plane, the y-intercept of the line [m]k[/m] is equal

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Carcass
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In the coordinate plane, the y-intercept of the line [m]k[/m] is equal [#permalink] New post   26 Mar 2021, 10:19
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In the coordinate plane, the y-intercept of the line \(k\) is equal to twice its slope. The y-intercept is not \(0\). What is the x-intercept of the line \(k\)?

A. -2
B. -1
C. 0
D. 1
E. 2

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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A
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Re: In the coordinate plane, the y-intercept of the line [m]k[/m] is equal [#permalink] New post   26 Mar 2021, 22:38
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Carcass wrote:
In the coordinate plane, the y-intercept of the line \(k\) is equal to twice its slope. The y-intercept is not \(0\). What is the x-intercept of the line \(k\)?

A. -2
B. -1
C. 0
D. 1
E. 2


Another Approach:

Equation of a line, \(y = mx + c\) and we are given \(c = 2m\)

So, \(y = mx + 2m\)
\(y = m(x + 2)\)

Plug \(y = 0\) for x-intercept;
\(0 = m(x + 2)\)
\((x + 2) = 0\)
\(x = -2\)

Hence, option A
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Re: In the coordinate plane, the y-intercept of the line [m]k[/m] is equal [#permalink] New post   26 Mar 2021, 10:25
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Carcass wrote:
In the coordinate plane, the y-intercept of the line \(k\) is equal to twice its slope. The y-intercept is not \(0\). What is the x-intercept of the line \(k\)?

A. -2
B. -1
C. 0
D. 1
E. 2

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


One approach is to choose some values that meet the given information.

In the coordinate plane, the y-intercept of the line k is equal to twice its slope.
Okay, so let's say the y-intercept of line k is 6. We get:
Image

Since the y-intercept (6) is TWICE the slope, we know that the slope = 3
Image

What is the x-intercept of the line k?
Since (x, 0) are the coordinates of the x-intercept . . .
Image
. . . we can apply the slope formula to wrote: (6 - 0)/(0 - x) = 3
Simplify: 6/(-x) = 3
Multiply both sides by -x to get: 6 = -3x
Solve: x = 6/(-3) = -2

Answer: A

Cheers,
Brent
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Re: In the coordinate plane, the y-intercept of the line [m]k[/m] is equal [#permalink] New post   30 Mar 2024, 13:01
Plug \(y = 0\) for x-intercept;
\(0 = m(x + 2)\)
\((x + 2) = 0\)
\(x = -2\)

Hello Karun, where did the m go?
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Re: In the coordinate plane, the y-intercept of the line [m]k[/m] is equal [#permalink] New post   30 Mar 2024, 15:05
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m IS A NUMBER. iT IS A COEFFICIENT

\(\frac{0}{m} = (x + 2)\)

\(\frac{0}{m}=0
\)
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Re: In the coordinate plane, the y-intercept of the line [m]k[/m] is equal [#permalink]
30 Mar 2024, 15:05
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