Step 1:The slope of a given line is $ m = -\frac{ 9 }{ 4 } $.

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

$$ m_1 = - \frac{1}{m} = -\frac{ 1 }{ -\frac{ 9 }{ 4 } } = \frac{ 4 }{ 9 } $$

So the perpendicular line will have a slope of $ m_1 = \frac{ 4 }{ 9 } $

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{ 4 }{ 9 } $ , $ x_0 = -3 $ and $ y_0 = 2 $. After substitution we have:

$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - 2 =& ~ \frac{ 4 }{ 9 } ( x - \left( -3\right)) \\y -2 =& ~ \frac{ 4 }{ 9 } x + \frac{ 4 }{ 3 } \\y =& ~ \frac{ 4 }{ 9 } x + \frac{ 4 }{ 3 } + 2 \\y =& ~ \frac{ 4 }{ 9 } x + \frac{ 10 }{ 3 }\\ \end{aligned} $$

Parallel and perpendicular lines calculator