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

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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

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

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 $$m(x+2)=0.$$

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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 $$k$$?

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

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

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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

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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

-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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