2:Here are four straight line equations. A.3y=4x+5 B.4y=3x-1 C.4y+3x=7 D.4x+3y=2 Which one of the following st

Question

2:Here are four straight line equations.
A.3y=4x+5
B.4y=3x-1
C.4y+3x=7
D.4x+3y=2
Which one of the following statements is true? Explain by working
A. Lines 1 and 2 are perpendicular
B. Lines 1 and 4 are parallel
C. Lines 2 and 4 are perpendicular
D. Lines 2 and 3 are parallel
E. I don’t know

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Genesis 1 week 2021-09-10T20:06:00+00:00 1 Answer 0 views 0

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    2021-09-10T20:07:04+00:00

    Answer:

    C. Lines 2 and 4 are perpendicular

    Step-by-step explanation:

    1. 3y = 4x + 5  => y = 4/3x + 5/3

    2. 4y = 3x – 1   => y = 3/4x – 1/4

    3. 4y + 3x = 7   => 4y = -3x + 7  => y = -3/4x + 7/4

    4. 4x + 3y = 2  => 3y = -4x + 2 => y = -4/3x + 2/3

    Comparing the above equations with y = mx+c,

    we find that the

    Slope of 1 (m1) = 4/3

    Slope of 2 (m2) = 3/4

    Slope of 3 (m3) = -3/4

    Slope of 4 (m4) = -4/3.

    We see that None of the slopes are equal to each other.

    So, no lines are parellel.

    Also, we see that m1*m3 = 4/3*-3/4 = -1

                                 m2*m4 = 3/4*-4/3 = -1

    We know, that the product of slopes of perpendicular lines = -1

    Hence, lines 1 and 3 are perpendicular and lines 2 and 4 are perpendicular.

    Note :- Opt. E. can also be justified as correct if it is true. 🙂

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