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Line L passes through the points (3, 4) and (6, 5) in the xy-plane. Wh

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Line L passes through the points (3, 4) and (6, 5) in the xy-plane. Wh [#permalink] New post   03 Jun 2021, 10:16
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Line \( \ell \) passes through the points (3, 4) and (6, 5) in the xy-plane. Which of the following could be the equation of a line parallel to line \(\ell\)?

Indicate all such equations.

A. \(y = 2x + 7\)

B. \(y = 3x – 4\)

C. \(y = \frac{1}{3} x – 5\)

D. \(y= \frac{1}{3} x + 2\)

E. \(y = 3x + 2\)

F. \(y = x – 3\)
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Re: Line L passes through the points (3, 4) and (6, 5) in the xy-plane. Wh [#permalink] New post   03 Jun 2021, 11:25
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Carcass wrote:
Line \( \ell \) passes through the points (3, 4) and (6, 5) in the xy-plane. Which of the following could be the equation of a line parallel to line \(\ell\)?

Indicate all such equations.

A. \(y = 2x + 7\)

B. \(y = 3x – 4\)

C. \(y = \frac{1}{3} x – 5\)

D. \(y= \frac{1}{3} x + 2\)

E. \(y = 3x + 2\)

F. \(y = x – 3\)


Key concept: Parallel lines have same slope

Let us find the slope of line \(l_1\), \(m = \frac{(5 - 4)}{(6 - 3)} = \frac{1}{3}\)

Therefore, equation of a line parallel to \(l_1\) will have an equation, \(y = \frac{1}{3}x + c\)

Hence, option C and D
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Re: Line L passes through the points (3, 4) and (6, 5) in the xy-plane. Wh [#permalink] New post   31 Aug 2024, 03:06
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Line L passes through the points (3, 4) and (6, 5) in the xy-plane. Wh [#permalink]
31 Aug 2024, 03:06
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