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In the xy plane

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In the xy plane  [#permalink]

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New post 05 Jul 2020, 06:10
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A
B
C
D
E

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Question Stats:

75% (01:36) correct 25% (01:17) wrong based on 8 sessions

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In the xy plane, if line k has a negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?

1) s=0
2) The y-intercept of the line k is negative

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Re: In the xy plane  [#permalink]

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New post 05 Jul 2020, 07:34
In the xy plane, if line k has a negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?

1) s=0 , since slope is negative m has negative value
y=mx+c
-2 = -m*0+c
c = -2

to determine x intercept, y has to be zero
0 = -mx -2
2 = -mx
x = -2/m
x intercept can't be positive (sufficient)

2) The y-intercept of the line k is negative.
that means C is negative
let say C is -2

to determine x intercept, y has to be zero
0 = -mx -2
2 = -mx
x = -2/m
x intercept can't be positive (sufficient)

Answer is D
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In the xy plane  [#permalink]

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New post 05 Jul 2020, 08:09
VERBAL1 wrote:
In the xy plane, if line k has a negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?

1) s=0
2) The y-intercept of the line k is negative

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Line k passes through the point (s,-2) and has negative slope
Concept tested -> If slope is negative, then line makes >90 degree angle and less than 180 degree angle with respect to z-axis when measured in anti-clockwise direction.
Hence we know that line's angle against z-axis lies in the above mentioned range.

Now let's analyse each statement

Statement 1 -> It says s=0, thus we know that the coordinate point lies below origin and on y-axis, and to maintain the negative slope, line has to maintain an angle that is greater than 90° but less than 180°. Clearly X intercept will be negative in this case, thus statement 1 is sufficient.
We can drop option B and E now.

Let's analyse statement 2
Statement 2 tells us that y intercept is negative, we can visualize this as the case when line k passes the XY plane below origin
And the case becomes same as statement -> s=0 -> (0,-2) means negative y intercept -> X is negative
Hence statement 2 is also sufficient.

Thus, both statements are sufficient independently

Our answer is option D
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Re: In the xy plane  [#permalink]

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New post 05 Jul 2020, 08:10
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Re: In the xy plane   [#permalink] 05 Jul 2020, 08:10

In the xy plane

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