The slope of line 1 is[tex]\frac{-2}{9}[/tex].
The slope of line 2 is[tex]\frac{-2}{9}[/tex].
The two lines are parallel.
Solution:
Points on line 1 are (10, 5) and (–8, 9).
[tex]x_1=10, y_1=5, x_2=-8, y_2=9[/tex]
Slope of line 1:
[tex]$m_1=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m_1=\frac{9-5}{-8-10}[/tex]
[tex]$m_1=\frac{4}{-18}[/tex]
[tex]$m_1=\frac{-2}{9}[/tex]
Points on line 2 are (2, –4) and (11, –6).
[tex]x_1=2, y_1=-4, x_2=11, y_2=-6[/tex]
Slope of line 2:
[tex]$m_2=\frac{-6-(-4)}{11-2}[/tex]
[tex]$m_2=\frac{-6+4}{9}[/tex]
[tex]$m_2=\frac{-2}{9}[/tex]
If slopes of the two lines are equal, then the two lines are parallel.
The slope of line 1 is[tex]\frac{-2}{9}[/tex].
The slope of line 2 is[tex]\frac{-2}{9}[/tex].
Hence the given two lines are parallel.
