Algebra 1

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Two lines L1 and L2, are perpendicular. The equation of L1 is 3x-y=2. L2 passes through (-5, -1)

  • Algebra 1 -

    Do you need to find L2?

    If two lines are perpendicular, the slope m of one is the negative reciprocal of the slope of the other,

    Slope m1 * m2 = -1
    or, slope m2 = -1/m1

    Your need to find slope m1 to write the equation of the perpendicular line.

    L1 = 3x - y = 2
    To find slope m, put the equation in slope-intercept form
    y = mx + b, where m = slope and b = y-intercept

    3x - y = 2
    y = 3x - 2
    So, slope m1 = 3

    Since, m2 = -1/m1 and m1 = 3,
    m2 = -1/3 = slope of L2 (perpendicular line)

    L2 through point (-5, -1)
    Form of the equation is,
    y = mx + b

    You found the slope m2 = -1/3
    y = -1/3 x + b

    To find b, use point (-5, -1) and substitute x and y point values in the equation and solve for b
    y = -1/3 x + b
    y = -5, x = -1
    -1 = -1/3 (-5) + b
    -1 = 5/3 + b
    b = -1 + -5/3
    b = -3/3 + -5/3
    b = -8/3

    So, L2 is
    y = -1/3 x + -8/3
    y = -1/3 x - 8/3

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