What is the equation of a line perpendicular to y-12=2x-3 that passes through the point (2, 3)?

Question

What is the equation of a line perpendicular to y-12=2x-3 that passes through the point (2, 3)?

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Sarah 3 weeks 2021-09-08T08:18:31+00:00 1 Answer 0

Answers ( )

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    2021-09-08T08:19:51+00:00

    Answer:

    y = – \frac{1}{2} x + 4

    Step-by-step explanation:

    The equation of a line in slope- intercept form is

    y = mx + c ( m is the slope and c the y- intercept )

    Given

    y – 12 = 2x – 3 ( add 12 to both sides )

    y = 2x + 9 ← in slope- intercept form

    with slope m = 2

    Given a line with slope m then the slope of a line perpendicular to it is

    m_{perpendicular} = – \frac{1}{m} = – \frac{1}{2}, thus

    y = – \frac{1}{2} x + c ← is the partial equation

    To find c substitute (2, 3) into the partial equation

    3 = – 1 + c ⇒ c = 3 + 1 = 4

    y = – \frac{1}{2} x + 4 ← equation of perpendicular line

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