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Math Help - Parallel and Perpendicular Lines

  1. #1
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    Parallel and Perpendicular Lines

    1. Find the slope of any line perpendicular to the line through points (0, 5) and (-3, -4).






    Write the equation of the line L satisfying the given geometric conditions.

    2. L has y-intercept (0, -3) and is parallel to the line with equation
    y = 2/3x + 1
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  2. #2
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    1.
    We know that the slope of a line that is perpindicular to the other is equal to the negative recipricol of the known slope. That is to say; if the slope of a line is 1/2 then the slope of a line perpindicular to the first is -2. Or more formally;
    m1.m2 = -1 ;where m1 and m2 are the respective slopes.

    So for this question, you just use the slope equation;
    m=(y2-y1)/(x2-x1)

    and apply the above theory.


    2.
    You know the slope of the line they've given you the equation for is 2/3 by y=mx+b. So therefore you know the slope of the line you want is also 2/3 as it is parallel (has the same slope). Now you just need to find the equation, they've given you a point, so just use the line formula;

    y-y1=m(x-x1)

    where y1 and x1 are your x and y points that are given to you and 'y' and 'x' are left as variables, rearrange the equation.



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