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In the coordinate plane, the y-intercept of the line k is equal to twi

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In the coordinate plane, the y-intercept of the line k is equal to twi  [#permalink]

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New post 16 Dec 2018, 23:40
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[Math Revolution GMAT math practice question]

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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Re: In the coordinate plane, the y-intercept of the line k is equal to twi  [#permalink]

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New post 17 Dec 2018, 00:30
MathRevolution wrote:
[Math Revolution GMAT math practice question]

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 \(k\)?

\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)



given c=2m

y=mx+c
or say
y=mx+2m
x= y/m-2

since y is not =0 , x intercept would be -2 ..
IMO A
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Re: In the coordinate plane, the y-intercept of the line k is equal to twi  [#permalink]

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New post 17 Dec 2018, 04:23
MathRevolution wrote:
[Math Revolution GMAT math practice question]

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 \(k\)?

\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)

\(k\,\,\,:\,\,\,y = ax + 2a\,\,\,\,\,\,\left( {a \ne 0} \right)\,\,\,\,\,\,\left( * \right)\)

\(?\,\,\,\,:\,\,\,{x_p}\,\,{\rm{when}}\,\,y = 0\)

\(\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,\,\,0 = a\left( {{x_p} + 2} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{a \ne 0} \,\,\,\,\,\,\,? = {x_p} = - 2\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: In the coordinate plane, the y-intercept of the line k is equal to twi  [#permalink]

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New post 17 Dec 2018, 06:23
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

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 \(k\)?

\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)


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 k is equal to twi  [#permalink]

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New post 17 Dec 2018, 07:19
MathRevolution wrote:
[Math Revolution GMAT math practice question]

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 \(k\)?

\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)


Equation of a line is y = mx +c
Since y intercept = twice of slope
So, c = 2m
y=mx+2m

TO find x intercept lets put y = 0
SO, mx+2m = 0
-> x = -2

Answer A
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Re: In the coordinate plane, the y-intercept of the line k is equal to twi  [#permalink]

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New post 19 Dec 2018, 05:00
=>

The equation of line \(k\) has the form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Let \(m\) be the slope of line \(k\). Then \(b = 2m\), and the equation is \(y = mx + 2m = m(x+2).\)
The x-intercept of line \(k\) is \(-2,\) since \(-2\) is a root of \(m(x+2)=0.\)

Therefore, the answer is A.
Answer: A
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Re: In the coordinate plane, the y-intercept of the line k is equal to twi &nbs [#permalink] 19 Dec 2018, 05:00
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