[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \parallel\ k\iff m_1=m_2\\\\\text{We have}\\\\L_1:y=5x+1\to m_1=5\\\\L_2:2y-10x-3=0\qquad\text{add 10x and 3 to both sides}\\\\L_2:2y=10x+3\qquad\text{divide both sides by 2}\\\\L_2:y=5x+1.5\to m_2=5\\\\m_1=m_2\ \text{therefore}\ l_1\ \text{and}\ L_2\ \text{are parallel.}[/tex]
