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parallell and perpendicular lines

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please check my homework

given P(7,2) and the line y + 3x=7 find the equation for the line

parallel line: y+3x+7
y=-3(x-7) +7
y-2=-3x+21+7
y=-3x+28+2
y=-3x+30

perpendicular line:
y-2=1/3(x-7) +7
y-2=1/3x-7/3 +21/3
y-2==1/3x + 14
y=1/3x + 14 +2
y=1/3x +16

  • parallell and perpendicular lines - ,

    Here is a neat way to do these question in a quicker way
    You should have learned that for a straight line equation in the form
    Ax + By = C, the slope of the line is -A/B

    so for 3x+y = 7 , a parallel line will differ only in the C value
    so new equation is
    3x + y = C
    plug in the point (7,2)
    21 + 2 = C = 23

    so new equation: 3x + y = 23 or y = -3x - 23

    notice the given point does not even satisfy your final equation.
    Your error is in the 2nd line, should be
    y = -3(x-7) + 2

    For the perpendicular short cut way:
    slope of given equation is -3
    so slope of perpendicular line is +1/3
    new equation:
    x - 3y = C, plug in the point (7,2)
    7 - 6 = C = 1
    x - 3y = 1 or y = (1/3)x - 1/3

    again, you made the error in the 2nd line, it should say
    y-2 = (1/3)(x-7)
    then 3y - 6 = x-7
    x - 3y = 1 , the same result as mine

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