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Math Help - An equation of the line containing the given point and perpendicular to the line

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    An equation of the line containing the given point and perpendicular to the line

    I need help with the steps and solving for an equation of the line containing the given point and perpendicular to the line:
    (5, -2); 9x + 8y =3
    I can find the slope (-8/9x?)... I just can't figure out the rest
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  2. #2
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    Quote Originally Posted by jay1 View Post
    I need help with the steps and solving for an equation of the line containing the given point and perpendicular to the line:
    (5, -2); 9x + 8y =3
    I can find the slope (-8/9x?)... I just can't figure out the rest
    The gradient of the normal to the line will be the negative reciprocal of the original gradient. That is, if your gradient is m, the gradient of the normal will be \frac{-1}{m}. Then, once you've found the gradient, substitute it, along with your point, into y-y_1=m(x-x_1) or y=mx+c to find the equation.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by jay1 View Post
    I need help with the steps and solving for an equation of the line containing the given point and perpendicular to the line:
    (5, -2); 9x + 8y =3
    I can find the slope (-8/9x?)... I just can't figure out the rest
    Hi jay1,

    The slope of 9x+8y=3 is not -\frac{8}{9}x

    Solve for y to put the equation in slope-intercept form ( y=mx+b where m is the slope):

    8y=-9x+3

    y=-\frac{9}{8}x+\frac{3}{8}

    Now do you know what the slope is?
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  4. #4
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    Quote Originally Posted by jay1 View Post
    I need help with the steps and solving for an equation of the line containing the given point and perpendicular to the line5, -2); 9x + 8y =3
    Here is a useful trick.
    Suppose that A\ne 0~\&~B\ne 0 then the lines
    Ax+By+C=0~\&~Bx-Ay+D=0
    are perpendicular.

    So for your problem just use your point in 8x-9y=k to find the value of k.
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  5. #5
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    You've got a point and the slope; go find out:
    Straight-Line Equations: Point-Slope Form
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