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

  1. #1
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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 $\displaystyle m$, the gradient of the normal will be $\displaystyle \frac{-1}{m}$. Then, once you've found the gradient, substitute it, along with your point, into $\displaystyle y-y_1=m(x-x_1)$ or $\displaystyle y=mx+c$ 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 $\displaystyle 9x+8y=3$ is not $\displaystyle -\frac{8}{9}x$

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

    $\displaystyle 8y=-9x+3$

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

    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 $\displaystyle A\ne 0~\&~B\ne 0$ then the lines
    $\displaystyle Ax+By+C=0~\&~Bx-Ay+D=0$
    are perpendicular.

    So for your problem just use your point in $\displaystyle 8x-9y=k$ 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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