If ab passes through the point (2,3) and is perpendicular to y=2x-7, find the equation of ab in general form. Show full working out ty

Question

If ab passes through the point (2,3) and is perpendicular to y=2x-7, find the equation of ab in general form.
Show full working out ty 😉

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Josie 2 weeks 2021-11-20T19:21:23+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-20T19:22:55+00:00

    Answer:

    x + 2y – 8 = 0

    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 )

    y = 2x – 7 ← is 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 in slope- intercept form

    The equation of a line in general form is

    Ax + By + C = 0 ( A is a positive integer and B, C are integers )

    Multiply the slope- intercept equation through by 2

    2y = – x + 8 ( add x to both sides )

    x + 2y = 8 ( subtract 8 from both sides )

    x + 2y – 8 = 0 ← in general form

    0
    2021-11-20T19:23:18+00:00

    Answer:

    2y + x = 8

    Step-by-step explanation:

    Since ab is perpendicular to the given line (with m1 = 2)

    m1×m2 = -1

    m2 = -½

    y = -½x + c

    When x = 2 , y = 3

    3 = -½(2) + c

    c = 3+1 = 4

    y = -½x + 4

    Multiply by 2

    2y = -x + 8

    2y + x = 8

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45:7+7-4:2-5:5*4+35:2 =? ( )