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In the coordinate plane, the y-intercept of the line k is eq

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by Max@Math Revolution » Sun Dec 16, 2018 11:30 pm

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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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by fskilnik@GMATH » Mon Dec 17, 2018 3:12 am
Max@Math Revolution 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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Brent@GMATPrepNow » Mon Dec 17, 2018 6:14 am
Max@Math Revolution 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
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Wed Dec 19, 2018 4:47 am
=>

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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by Scott@TargetTestPrep » Sun Mar 03, 2019 6:30 pm
Max@Math Revolution 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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