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In the xy-plane, line/ is parallel to the line y = 3x + 2. I

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In the xy-plane, line/ is parallel to the line y = 3x + 2. I [#permalink] New post 20 Nov 2019, 04:28
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In the xy-plane, line \(\ell\) is parallel to the line \(y = 3x + 2\). If line \(\ell\) passes through the point (1, —1), then line \(\ell\) passes through which of the following points?


Indicate all such points.


A. (2, 2)

B. (0, -2)

C. (-2, -10)


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[Reveal] Spoiler: OA

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Re: In the xy-plane, line/ is parallel to the line y = 3x + 2. I [#permalink] New post 23 Nov 2019, 16:12
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We have to determine the equation of line l.
Since line l is parallel to the line \(y=3x+2\), the two lines have the same slope.
By using the given coordinates (1, -1) we can determine the y-intercept of line l.
The equation of l is Y(l)=3x-4
Finally, we have to plug in A, B, and C to find the solution.
Answer A and C are correct
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Re: In the xy-plane, line/ is parallel to the line y = 3x + 2. I [#permalink] New post 22 Jun 2020, 18:03
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In the xy-plane, line ℓ is parallel to the line y=3x+2y. If line ℓ passes through the point (1, —1), then line ℓ passes through which of the following points?

Since line l is parallel to line y therefore the slopes are equal i.e. m=3
line l points are (1,-1), put these points in the given equation of y to get the y-intercept
y=mx+c
-1=3(1)+c
c=-4 (y-intercept)
now the equation is:
y=3x-4
now put the values of given options:
A. (2,2)
x=2
y=3x-4
y=3(2)-4
y=2
Hence (x,y) = (2,2) this is correct

Similarly check B and C. Only A and C are correct options
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Re: In the xy-plane, line/ is parallel to the line y = 3x + 2. I   [#permalink] 22 Jun 2020, 18:03
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In the xy-plane, line/ is parallel to the line y = 3x + 2. I

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