Question
Find the line that is parallel to $ y = 6 x + 2 $ and passes though the point $ \left(3,~-1\right) $.
Answer
The equation of the line parallel to the given line that contains point $ A $ is:
$ \color{blue}{ 6x-y-19=0 }$ ( General form )
$ \color{blue}{ y = 6 x - 19 } ~~~$ ( Slope y-intercept form )
Explanation
Step 1:The slope of a given line is $ m = 6 $.
Step 2: Parallel lines have the same slope, so the slope of the unknown line ($ m_1 $) will also be $ 6 $. So the parallel line will have a slope of $ m_1 = 6 $
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 = 6 $ , $ x_0 = 3 $ and $ y_0 = -1 $. After substitution we have:
$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - \left( -1\right) =& ~ 6 ( x - 3) \\y + 1 =& ~ 6 x -18 \\y =& ~ 6 x -18 -1 \\y =& ~ 6 x - 19\\ \end{aligned} $$This page was created using
Parallel and perpendicular lines calculator