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Math Help - perpendicular, slope and y-intercept

  1. #1
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    perpendicular, slope and y-intercept

    1. Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = 3x + 1.




    2. Write the equation of the line that passes through point (7, 9) with a slope of 2




    3. Find the slope and y-intercept.
    2x + 10y = 20
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  2. #2
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    1. Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = 3x + 1.

    You're given the slope of a line y=-3x +1, is obviously -3. Therefore the perpindicular line you are trying to find has slope 1/3. Now you have the slope and a point on the line, use the line formula y-y1=m(x-x1) and rearrange.

    y-5=(1/3)(x-0)
    y-5=(1/3)x
    y=(1/3)x + 5



    2. Write the equation of the line that passes through point (7, 9) with a slope of 2

    Simpler than above, just use the line formula;
    y-y1=m(x-x1)
    y-9=-2(x+7)
    y-9=-2x + 7
    y=-2x +7+9
    y=-2x +16

    3. Find the slope and y-intercept.
    2x + 10y = 20

    rearrange for and make y the subject, the coefficient of x is the slope and the added constant is the y-coordinate of the y-intercept;

    -2x+10y=-20
    10y=2x-20
    y=(1/5)x -4

    therefore the slope is 1/5 and the y intercept is (0,-4)


    ------------------

    remember the key concepts here; the relationship of slopes between perpindicular and parallel lines, how to use the line and slope formulas; and recognising the form y=mx+b in finding slopes and y-intercepts.
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