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In the x-y coordinate plane, line k passes through the point (5, -4)

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In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

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New post 16 Oct 2018, 04:55
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In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only

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Re: In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

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New post 16 Oct 2018, 05:33
GMATPrepNow wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only





The answer should be equation 1 only.
By putting the value of (5,-4) in all the three equations, we can eliminate the 3rd equation.
SInce the x intercept is negative, equation 2 cannot be the answer. When we put x=0 in equation 2, x assumes a positive value.

SO equation 1 is the only correct.
SO answer should be Option A.
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Re: In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

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New post 16 Oct 2018, 05:35
GMATPrepNow wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only


As per Question stem, X-intercept is negative. Hence put Y=0 in every equation to check if X-intercept is negative or not.
(I)> y=-0.4x-2 => Putting Y=0, we get - X intercept= NEGATIVE
(II)> y = 2 - 1.2x => Putting Y=0, we get -X intercept= POSITIVE
(III)> y = -0.7x - 1.5 => Putting Y=0, we get - X intercept= NEGATIVE

Hence, Statement (I) & (III) satisfies, this criteria i.e. X intercept is negative

Now Check whether point (5, -4) lies on these equations or not.
(I)> y=-0.4x-2 => Putting X=5 & Y=-4, Both LHS & RHS are equal, hence This point lies on this equation. Statement (I) satisfies.
(II)> y = 2 - 1.2x => Putting X=5 & Y=-4, Both LHS & RHS are equal, hence This point lies on this equation. Statement (II) satisfies.
(III)> y = -0.7x - 1.5 => Putting X=5 & Y=-4, Both LHS & RHS are not equal, hence This point doesn't lie on this equation. Statement (III) doesn't satisfies.

Hence, Statement (I) & (II) satisfies, this criteria i.e. point (5,-4) lies on the given line.

Taking both criteria into consideration, we get, only Statement (I) satisfies both the criteria. Hence, correct answer should be A.
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Re: In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

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New post 16 Oct 2018, 11:18
GMATPrepNow wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only

Reminder (to my students) / Suggestion (to the general reader):

1. One property at a time, till the end. Then the other. ("Don´t let your brain dance!")

2. Start with the easier checking property (or the one you feel more comfortable).
Indifferent? Start with the first.

\(?\,\,\left( 1 \right)\,\,\,\,:\,\,\,\,\left( {5, - 4} \right)\,\,\mathop \in \limits^? \,\,\,{\text{line}}\,\,\)

\(\left( i \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{2}{5}\left( 5 \right) - 2\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\)

\(\left( {ii} \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{6}{5}\left( 5 \right) + 2\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\)

\(\left( {iii} \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{7}{{10}}\left( 5 \right) - \frac{3}{2}\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( C \right),\,\,\left( E \right)\)


\(?\,\,\left( 2 \right)\,\,\,\,:\,\,\,\,{\text{line}}\,\,x - {\text{intercept}}\,\,\,\mathop < \limits^? \,\,0\)

\(\left( i \right)\,\,0\, = \,\, - \frac{2}{5}\left( x \right) - 2\,\,\,\,\,\mathop \Rightarrow \limits^? \,\,\,x < \,\,0\,\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( B \right)\)

\(\left( {ii} \right)\,\,0\, = \,\, - \frac{6}{5}\left( x \right) + 2\,\,\,\,\,\mathop \Rightarrow \limits^? \,\,\,x < \,\,0\,\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( D \right)\)


The correct answer is (A).


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

Regards,
Fabio.
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Re: In the x-y coordinate plane, line k passes through the point (5, -4)  [#permalink]

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New post 18 Oct 2018, 09:36
Top Contributor
GMATPrepNow wrote:
In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?

i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5

A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only


Notice that, if the line passes through the origin, then the line has slope -4/5 (aka a slope of -0.8), but the line will not have a negative x-intercept
Notice that, if the line passes through the (0,4), then the line will have slope 0, BUT the line will not have a negative x-intercept. See below.
Image

So, if the slope of the line is BETWEEN 0 and -0.8, then the line will have a negative x-intercept


Check the 3 statements:
i) y = -0.4x - 2
The slope = -0.4, which is BETWEEN 0 and -0.8. KEEP i for now

ii) y = 2 - 1.2x
Rewrite as: y = -1.2 + 2.
The slope = -1.2, which is NOT BETWEEN 0 and -0.8. So, ii cannot be true

iii) y = -0.7x - 1.5
The slope = -0.7, which is BETWEEN 0 and -0.8. KEEP iii for now

So far, i and iii COULD both be true.

However, in order for the point (5, -4) to be ON line k, its x and y coordinates must satisfy the equation of the line.
So, let's check i and iii

i) y = -0.4x - 2
Plug in x = 5 and y = -4 to get: -4 = -0.4(5) - 2 = -2 - 2 = -4
PERFECT!
So, i is true

iii) y = -0.7x - 1.5
Plug in x = 5 and y = -4 to get: -4 = -0.7(5) - 1.5 = -3.5 - 1.5 = -5
NO GOOD
So, iii is not true

Answer: A

Cheers,
Brent
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Re: In the x-y coordinate plane, line k passes through the point (5, -4) &nbs [#permalink] 18 Oct 2018, 09:36
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In the x-y coordinate plane, line k passes through the point (5, -4)

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