Question 1019903
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Hi 
Note:  the standard slope-intercept form for an equation of a line is 
{{{y = highlight_green(m)x + highlight(b)}}}  where m is the slope and b the y-intercept.  
It is as simple as solving the first of the two for y and comparing their slopes
-14x = -632 - 26y   0r {{{y = highlight_green(14/26)x - highlight(632)}}}
 y = (7/13)x - 316/13  Lines are parallel {{{14/26 = 7/13}}}

5x + 4y = -60 0r {{{y = highlight_green(5/4)x - highlight(15)}}}
 y = (-4/5)x - (3/5) Lines are perpendicular {{{(-4/5)(5/4) = -1}}} negative reciprocals

-2y = -380 + 14x  0r {{{y = highlight_green(-7)x + highlight(190)}}} 
 y = -7x + 190 Lines are parallel {{{-7 = -7}}}