# Finding the equation of a line

• Jan 31st 2009, 11:36 AM
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.
• Jan 31st 2009, 11:44 AM
red_dog
$\displaystyle x-8y=2\Rightarrow y=\frac{1}{8}x-\frac{1}{4}\Rightarrow m=\frac{1}{8}\Rightarrow m'=-\frac{1}{m}=-8$

Here m' is the slope of the perpendicular.
The equation is $\displaystyle y-y_0=m'(x-x_0)$ where $\displaystyle (x_0,y_0)=(-8,9)$
• Jan 31st 2009, 11:48 AM
masters
Quote:

Find the slope-intercept equation of the line that passes through (-8, 9) and is perpendicular to x - 8y = 2.

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:

$\displaystyle y=-8x-55$