Question 917810

you got

line 1.    {{{y=2}}} 
line 2.   {{{y= (1/5)x-3}}}
line 3.    {{{y=-4}}}
line 4.  {{{y= -5(x+2) }}}

by definition, perpendicular lines have slopes negative reciprocal to each other


line 1.    {{{y=2}}} ....slope is zero, line is parallel to x-axis
line 2.   {{{y=highlight(-(1/5))x-3}}}... slope is {{{m[1]=1/5}}}
line 3.    {{{y=-4}}}....slope is zero, line is parallel to x-axis
line 4.  {{{y= highlight(-5)(x+2)}}}........slope is {{{m[2]=-5}}}

check if {{{m[1]=-1/m[2]}}}; if yes, then lines are perpendicular

{{{1/5=-1/(-5)}}} 

{{{1/5=1/5}}} ...true, so lines 2 and 4 are perpendicular

{{{ graph( 600, 600, -10, 10, -10, 10, (1/5)x-3, -5(x+2)) }}}