Pre- Algebra

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Given an equation of a line, how do I find equations for lines parallel to it going through specified points Simplifying the equations into slope-intercept form.
1. y= -2x -4; (1, 3) how do I write the equation of a line parallel to the given line but passing through the given point
2. y= 3x + 3; (1,1) how do I write the equation of a line perpendicular to the given line but passing through the given point

  • Algebra -

    It must have the same slope: -2
    Now you have a point and a slope, so the line is
    y-3 = -2(x-1)

    same idea, but you want the perpendicular slope, which is the negative reciprocal of the line's slope: -1/3
    y-1 = -1/3(x-1)

    review the various forms of the equation of a line:

    standard
    point-slope
    two-point
    slope-intercept

  • Pre- Algebra -

    1. Y = -2x - 4. (1,3).
    Parallel lines have equal slopes:
    m1 = m2 = -2.

    Y = mx + b = 3
    -2*1 + b = 3
    b = 3+2 = 5
    Eq: Y = -2x + 5

    2. Y = 3x+3. (1,1).
    The slope of the line is equal to the negat1ive reciprocal of the slope of the given line.
    m1 = 3
    m2 = -1/3.

    Y = mx + b = 1
    (-1/3)*1 + b = 1
    b = 1 + 1/3 = 1 1/3 = 4/3

    Eq: Y = (-1/3)x + 4/3

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