Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line}:\\\\y=mx+b\\\\m-\text{slope}\\b-\text{y-intercept}\\\\\text{Let}\\\\k:y=m_1x+b_1\\l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\=======================[/tex]
[tex]\text{Parallel lines have the same slope}.\\\\\text{We have}\ y=2(x+3)-4=(2)(x)+(2)(3)-4=2x+6-4=2x+2\\\\\text{The slope}\ m=2.\\\\\text{All parallel lines to the given line have the equation:}\\\\y=2x+b\\\\\text{where}\ b\ \text{is any real number except 2}.[/tex]
