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

Question

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

nitesh50 · Answer

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.

AnupamKT · Answer

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.

fskilnik · Answer

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 ight)\,\,\,\,:\,\,\,\,\left( {5, - 4} ight)\,\,\mathop \in \limits^? \,\,\,{	ext{line}}\,\,

\left( i ight)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{2}{5}\left( 5 ight) - 2\,\,\,\,\,\,\left\langle {{	ext{YES}}} ightangle \,

\left( {ii} ight)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{6}{5}\left( 5 ight) + 2\,\,\,\,\,\,\left\langle {{	ext{YES}}} ightangle \,\,

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

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

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

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

The correct answer is (A).

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

Regards, 
Fabio.

BrentGMATPrepNow · Answer

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.
 https://i.imgur.com/c9EA05O.png

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

Scuven · Answer

We can at fist eliminate option II since if the line passes through its y intercept (substitute x=0 and obtain y=2) the line cannot pass also through a negative x intercept starting from point (5,-4)

Then we proceed by substituting the point on the equations to see if the line passes throigh the point and we obtain only I

bumpbot · Answer

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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)

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