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25 June, 21:21

Find the equation in slope intercept form and standard form of the line that passes through (4,-3) and is perpendicular to 3x-y=5.

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  1. 25 June, 23:20
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    The given line is y = 3x - 5 after adding Y and subtracting 5 from both sides.

    The slope of this given line is 3.

    Therefore, the slope of the perpendicular line is - 1/3, as it must be the negative reciprocal.

    The general form of a line equation in slope intercept form is y = Mx+B where M is the slope and B is the intercept.

    Solving for B is: B = y - Mx

    So the intercept of the perpendicular line with slope M=-1/3 and passing through (x=4, y=-3) is

    y M * x

    B = - 3 - (-1/3) * 4 =

    -3 + 1/3*4 = <- - subtracting the negative is the same as adding the positive; definition of subtraction

    -3 + 4/3 = <- - multiplies the fractions first per order of mixed operations

    -9/3 + 4/3 <- - common denominator is 3

    = - 5/3

    So the equation of the perpendicular line is y = - 1/3X + - 5/3 = - 1/3X-5/3

    Notice when X=4, y = - 1/3 (4) - 5/3 = - 4/3 - 5/3 = - 9/3 = - 3 as expected
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