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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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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.

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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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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]
Expert Reply
=>

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 [#permalink]
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Expert Reply
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 \(k\)?

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


We can let m = the slope, and thus 2m = the y-intercept. The equation of the line is

y = mx + 2m

To find the x-intercept, we set y = 0 and solve for x. Thus, we have:

0 = mx + 2m

-mx = 2m

Since the y-intercept is non-zero, m is non-zero as well. Thus, we can divide each side by -m:

x = 2m/(-m)

x = 2/(-1) = -2

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

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



slope, m=-y/x (1)
Given, y=2m (2)
sustitute (2) in (1),
m=-2m/x
ie., x=-2

answer is 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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Slope of a line is given by:

(-) (Y-intercept) / (X-intercept)

Let the x-intercept = a

Let the y-intercept = b

m = (-b) / (a)

And

b = 2m

b = 2 * (-b / a)

Since the y-intercept is not 0, the line does not pass through the origin, resulting in the x-intercept (a) being non-zero as well

Cancel the b variable in the numerator and cross multiply:

1 = -2 / a

a = -2

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