Question

The lines given by the equations y=2x and y=4x+1 are

Answer 1

the equations are already in slope-intercept form, therefore

$\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\stackrel{\stackrel{slope}{\downarrow }}{m}x+\stackrel{\stackrel{y-intercept}{\downarrow }}{b}\\\\ y=mx+b \\\\ \cline{1-1} \end{array}~\hspace{8em}y=\stackrel{slope}{2}x\qquad y=\stackrel{slope}{4}x+1$

so their slopes are 2 and 4.

parallel lines have exactly the same slope, these ones do not, so they're not parallel.

perpendicular lines, have negative reciprocal slopes, in short, their product gives -1, 2*4 ≠ -1, so they're not perpendicular either.