Step 1:The slope of a given line is $ m = \frac{ 10 }{ 3 } $.

Step 2: Parallel lines have the same slope, so the slope of the unknown line ($ m_1 $) will also be $ \frac{ 10 }{ 3 } $. So the parallel line will have a slope of $ m_1 = \frac{ 10 }{ 3 } $

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{ 10 }{ 3 } $ , $ x_0 = -3 $ and $ y_0 = -2 $. After substitution we have:

$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - \left( -2\right) =& ~ \frac{ 10 }{ 3 } ( x - \left( -3\right)) \\y + 2 =& ~ \frac{ 10 }{ 3 } x + 10 \\y =& ~ \frac{ 10 }{ 3 } x + 10 -2 \\y =& ~ \frac{ 10 }{ 3 } x + 8\\ \end{aligned} $$

Parallel and perpendicular lines calculator