Question 1126473
to see is {{{y=-(7/8)x+3 }}} and {{{-7y=-8x}}} perpendicular, first write {{{-7y=-8x}}} in slope-intercept form

{{{y=(-8/-7)x}}}

{{{y=(8/7)x}}}

compare their slopes:

{{{y=-highlight((7/8))x+3 }}}

{{{y=highlight((8/7))x}}}

as you can see, {{{highlight((8/7))}}} is negative reciprocal of {{{-highlight((7/8))}}}

or {{{highlight((8/7))=-1/highlight(-(7/8))}}}

by definition, lines are  perpendicular {{{if}}} their slopes are negative reciprocal to each other


{{{drawing( 600, 600, -10, 10, -10, 10,
locate(-4,4,y=-(7/8)x+3),locate(4,5,y=(8/7)x),
 graph( 600, 600, -10, 10, -10, 10, -(7/8)x+3, (8/7)x)) }}}