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Thread: Finding the equation of a line

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    Finding the equation of a line

    Find the slope-intercept equation of the line that passes through (-8, 9) and is perpendicular to x - 8y = 2.
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    MHF Contributor red_dog's Avatar
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    $\displaystyle x-8y=2\Rightarrow y=\frac{1}{8}x-\frac{1}{4}\Rightarrow m=\frac{1}{8}\Rightarrow m'=-\frac{1}{m}=-8$

    Here m' is the slope of the perpendicular.
    The equation is $\displaystyle y-y_0=m'(x-x_0)$ where $\displaystyle (x_0,y_0)=(-8,9)$
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by keadyjr View Post
    Find the slope-intercept equation of the line that passes through (-8, 9) and is perpendicular to x - 8y = 2.
    Hi keadyjr,

    First of all find the slope of your line given by the equation x - 8y = 2. Let's put it in slope-intercept form:

    $\displaystyle y=\frac{1}{8}x-\frac{1}{4}$

    So the slope is $\displaystyle \frac{1}{8}$

    The slope of a line perpendicular to this line would be the negative reciprocal of $\displaystyle \frac{1}{8}$, or $\displaystyle -8$.

    Using the point (-8, 9) and a slope of -8, we can now find the y-intercept.

    $\displaystyle y=mx+b$

    $\displaystyle 9=-8(-8)+b$

    $\displaystyle b=-55$

    Substituting back into the slope intercept form, we arrive at:

    $\displaystyle y=-8x-55$
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