69.6k views
4 votes
Which equations of the three lines are parallel, perpendicular, or neither?

Which equations of the three lines are parallel, perpendicular, or neither?-example-1

1 Answer

4 votes

The given lines are


6x-4y=8;y=(3)/(2)x+6;2y=3x+5

Convert each equation in the form


y=mx+c_{}

Therefore it follows:


\begin{gathered} 6x-4y=8\Rightarrow y=(3)/(2)x+2 \\ y=(3)/(2)x+6\Rightarrow y=(3)/(2)x+6 \\ 2y=3x+5\Rightarrow y=(3)/(2)x+(5)/(2) \end{gathered}

Therefore the slopes of all three lines are:


\begin{gathered} m_1=(3)/(2) \\ m_2=(3)/(2) \\ m_3=(3)/(2) \end{gathered}

The slopes of all three lines are equal therefore all three lines are parallel with each other.

Therefore it follows that:


l_1\parallel l_2\parallel l_3

Which equations of the three lines are parallel, perpendicular, or neither?-example-1
User Schalkneethling
by
7.3k points