Question
Find the line that is perpendicular to $ y = x - \frac{ 1 }{ 3 } $ and passes though the point $ \left(0,~0\right) $.
Answer
The equation of the line perpendicular to the given line that contains point $ A $ is:
$ \color{blue}{ x+y=0 }$ ( General form )
$ \color{blue}{ y = - x } ~~~$ ( Slope y-intercept form )
Explanation
Step 1:The slope of a given line is $ m = 1 $.
Step 2: The perpendicular slope ($ m_1 $) is negative reciprocal of the slope $ m $.
$$ m_1 = - \frac{1}{m} = -\frac{ 1 }{ 1 } = -1 $$So the perpendicular line will have a slope of $ m_1 = -1 $
Step 3: Now we have a point and the slope so we can use point-slope form, which is:
$$ y - y_0 = m_1 (x - x_0) $$In this example we have: $ m_1 = -1 $ , $ x_0 = 0 $ and $ y_0 = 0 $. After substitution we have:
$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - 0 =& ~ -1 ( x - 0) \\y =& ~ - x\\ \end{aligned} $$This page was created using
Parallel and perpendicular lines calculator