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Which of the following lines is parallel to line x = 2.5 - 2y ?

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Which of the following lines is parallel to line x = 2.5 - 2y ? [#permalink] New post   28 Jan 2021, 13:11
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A
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C
D
E

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Which of the following lines is parallel to line \(x = 2.5 - 2y\) ?


A. \(y = 2x + 25\)

B. \(y= \frac{8}{3}x - 2\)

C. \(x + 3y = 0\)

D. \(y = -\frac{1}{2}x - 32\)

E. \(y = \frac{1}{2}x + 3\)
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D
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Re: Which of the following lines is parallel to line x = 2.5 - 2y ? [#permalink] New post   28 Jan 2021, 18:30
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Isolating y and getting the line in the form of y = mx + c, we get \(y = -\frac{1}{2}x - 1.25\).

The equation of a line parallel to this should have the same slope (-1/2), but with a different constant term.


Option D

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Which of the following lines is parallel to line x = 2.5 - 2y ? [#permalink] New post   28 Jan 2021, 20:04
\(Paralles \ lines \ have \ an \ equal \ slope, m_1=m_2\)

\(Perpendicular \ lines \ have \ negative \ reciprocal \ slopes, m_1 = -\frac{1}{m_2}\)

Given equation;
\(x= \frac{5}{2}-2y\)

\(2y=-x+\frac{5}{2}\)

\(y=-\frac{1}{2}x+\frac{5}{4}\)

\(m_1 = -\frac{1}{2}=m_2\)

\(Equation \ of \ the \ 2^{nd} \ line, y=m_2x+c=-\frac{1}{2}x+c\)

Only option D satisfies \(m_2=-\frac{1}{2} \) ; \(y=−\frac{1}{2}x−32 \)
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Re: Which of the following lines is parallel to line x = 2.5 - 2y ? [#permalink] New post   31 Jan 2021, 06:21
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Solution



Given
In this question, we are given
    A line with equation x=2.5−2y

To find
We need to determine
    The line in the answer choices that is parallel to the given line

Approach and Working out

    x = 2.5−2y
      2y = 2.5 – x
      y = 1.25 - 1/2x
        Comparing with the slope-intercept form y = mx + c, we can say that the given line has slope = -1/2 and y-intercept = 1.25

    Two parallel lines have the same slope but different y-intercepts.
      The only answer choice that has -1/2 as slope is D.

Thus, option D is the correct answer.

Correct Answer: Option D
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Re: Which of the following lines is parallel to line x = 2.5 - 2y ? [#permalink]
31 Jan 2021, 06:21
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