Identify the pair of lines as parallel or perpendicular. 1. f(x) = 2x + 3 g(x) = -1/2x + 3 2. f(x) = 1/3x + 4

Question

Identify the pair of lines as parallel or perpendicular.
1. f(x) = 2x + 3
g(x) = -1/2x + 3

2. f(x) = 1/3x + 4
g(x) = 1/3x + 5

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Harper 2 weeks 2021-09-10T08:27:56+00:00 2 Answers 0

Answers ( )

    0
    2021-09-10T08:29:01+00:00

    Answer:

    1. perpendicular

    2. parallel

    Step-by-step explanation:

    \text{Let}\\\\k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\\text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2

    1.\\f(x)=2x+3\to m_1=2\\\\g(x)=-\dfrac{1}{2}x+3\to m_2=-\dfrac{1}{2}\\\\m_1\neq m_2\\\\m_1m_2=(2)\left(-\dfrac{1}{2}\right)=-\dfrac{2}{2}=-1\\\\Answer:\ \text{lines are perpendicular}

    2.\\f(x)=\dfrac{1}{3}x+4\to m_1=\dfrac{1}{3}\\\\g(x)=\dfrac{1}{3}x+5\to m_2=\dfrac{1}{3}\\\\m_1=m_2\\\\Answer:\ \text{lines are parallel}

    0
    2021-09-10T08:29:19+00:00

    Answer:

    1.  Perpendicular

    2.  Parallel

    Step-by-step explanation:

    A line is parallel to another if it has the same slope

    A line is perpendicular to another if it has the opposite reciprocal of the other slope.

    1.  f(x) = 2x + 3

       f(xx) = -1/2 + 3

    Perpendicular

    2.  f(x) = 1/3x + 4

        g(x) = 1/3x + 5

    Parallel

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