Question
Find the line that is parallel to $ y = - \frac{ 2 }{ 5 } x + 4 $ and passes though the point $ \left(-3,~2\right) $.
Answer
The equation of the line parallel to the given line that contains point $ A $ is:
$ \color{blue}{ 2x+5y-4=0 }$ ( General form )
$ \color{blue}{ y = - \dfrac{ 2 }{ 5 } x + \dfrac{ 4 }{ 5 } } ~~~$ ( Slope y-intercept form )
Explanation
Step 1:The slope of a given line is $ m = -\frac{ 2 }{ 5 } $.
Step 2: Parallel lines have the same slope, so the slope of the unknown line ($ m_1 $) will also be $ -\frac{ 2 }{ 5 } $. So the parallel line will have a slope of $ m_1 = -\frac{ 2 }{ 5 } $
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{ 2 }{ 5 } $ , $ x_0 = -3 $ and $ y_0 = 2 $. After substitution we have:
$$ \begin{aligned} y - y_0 =& ~ m_1 (x - x_0) \\ y - 2 =& ~ -\frac{ 2 }{ 5 } ( x - \left( -3\right)) \\y -2 =& ~ -\frac{ 2 }{ 5 } x -\frac{ 6 }{ 5 } \\y =& ~ -\frac{ 2 }{ 5 } x -\frac{ 6 }{ 5 } + 2 \\y =& ~ - \frac{ 2 }{ 5 } x + \frac{ 4 }{ 5 }\\ \end{aligned} $$This page was created using
Parallel and perpendicular lines calculator