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  1. #1
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    find linear function

    Find the equation of the line thru (1-1) that is parallel to 3x+2y=1
    Last edited by lemontea; May 7th 2008 at 08:33 PM.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by lemontea View Post
    Find the equation of the line thru (1-1) that is parallel to 3x+2y=1
    There are two different ways on finding the equation of the line. Pick the one that is better for you:

    First Way

    First solve the equation 3x+2y=1 for y. You should get y=-\frac{3}{2}x+\frac{1}{2}. If the lines are parallel, then the new line with have the same slope. Since the new line must pass through (1,-1), we can substitute these values into the point-slope form of a line.

    Point slope form: y-y_1=m(x-x_1)

    (y-(-1))=(-\frac{3}{2})(x-(1))\rightarrow y=-\frac{3}{2}x+\frac{3}{2}-1\rightarrow y=-\frac{3}{2}x+\frac{1}{2}

    Second Way

    First solve the equation 3x+2y=1 for y. You should get y=-\frac{3}{2}x+\frac{1}{2}. If the lines are parallel, then the new line with have the same slope. We can substitute the value of the slope into the slope intercept form of a line:

    Slope intercept form: y=mx+b

    y=-\frac{3}{2}x+b.

    To find b, plug in the point (1,-1)

    -1=-\frac{3}{2}(1)+b\rightarrow -1+\frac{3}{2}=b\rightarrow b=\frac{1}{2}.

    Thus the equation of the line is y=-\frac{3}{2}x+\frac{1}{2}.

    Hope this helped you out!
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