Step 1:The slope of a given line is $ m = \frac{ 2 }{ 3 } $.

Step 2: The perpendicular slope ($ m_1 $) is negative reciprocal of the slope $ m $.

$$ m_1 = - \frac{1}{m} = -\frac{ 1 }{ \frac{ 2 }{ 3 } } = -\frac{ 3 }{ 2 } $$

So the perpendicular line will have a slope of $ m_1 = -\frac{ 3 }{ 2 } $

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 = -\frac{ 3 }{ 2 } $ , $ x_0 = -4 $ and $ y_0 = 1 $. After substitution we have:

$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - 1 =& ~ -\frac{ 3 }{ 2 } ( x - \left( -4\right)) \\y -1 =& ~ -\frac{ 3 }{ 2 } x -6 \\y =& ~ -\frac{ 3 }{ 2 } x -6 + 1 \\y =& ~ - \frac{ 3 }{ 2 } x - 5\\ \end{aligned} $$

Parallel and perpendicular lines calculator