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Line l is defined by

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Carcass
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Line l is defined by [#permalink] New post   04 Mar 2021, 02:37
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Line \(\ell\) is defined by the equation \(y=2x+3\)

Line \(m\) intersects line \(\ell\) at the point \((6,9)\)

Quantity A
Quantity B
The slope of line \(\ell\)
The slope of line \(m\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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D
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Re: Line l is defined by [#permalink] New post   04 Mar 2021, 06:13
Slope of line L can be found by comparing the equation with y=mx+c, where m = slope

However, no details for line m is given. Only point of intersection is not enough to find the slope.

Hence Answer D
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Re: Line l is defined by [#permalink] New post   04 Mar 2021, 07:53
Carcass wrote:
Line \(\ell\) is defined by the equation \(y=2x+3\)

Line \(m\) intersects line \(\ell\) at the point \((6,9)\)

Quantity A
Quantity B
The slope of line \(\ell\)
The slope of line \(m\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation


Carcass
Are you sure the question is correct?
The question says \(m\) and \(l\) intersect at (6,9) - But \(y = 2x + 3\) will never cross (6,9)!!
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Re: Line l is defined by [#permalink] New post   04 Mar 2021, 10:08
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OE

We know that the slope of line l is 2, but knowing the point of intersection is not enough to learn anything about the slope of line m . Therefore, a relationship between the two quantities cannot be determined.

Yes the stem is correct KarunMendiratta
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Re: Line l is defined by [#permalink] New post   04 Mar 2021, 10:41
Carcass wrote:
OE

We know that the slope of line l is 2, but knowing the point of intersection is not enough to learn anything about the slope of line m . Therefore, a relationship between the two quantities cannot be determined.

Yes the stem is correct KarunMendiratta


The OA must be D. But I'm just asking that the question says line \(l\) and line \(m\) intersect at (6,9), right?
So (6,9) must also lie on line \(l\)

y = 2x + 3
When x = 6, y = 15
How?
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Re: Line l is defined by [#permalink] New post   04 Mar 2021, 17:14
1
The official solution is correct to say that knowing the point of intersection is not enough to learn anything about the slope of a line.

However, the official solution is incorrect when it suggests the point (6, 9) lies on the line defined by y = 2x + 3
In order for any point to lie on the line y = 2x + 3, the x and y coordinates of that point must satisfy the given equation.
So, if (6, 9) lies on the line, then it must be the case that: 9 = 2(6) + 3
When we simplify this we get: 9 = 15
So, the point (6, 9) does not lie on the line defined by y = 2x + 3

If the equation of the line were rewritten as y = 2x - 3, then everything would be mathematically correct, and the answer would be D
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Re: Line l is defined by [#permalink] New post   05 Mar 2021, 00:31
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Thank you Sir
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Re: Line l is defined by [#permalink]
05 Mar 2021, 00:31
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