Question 970369

Which best describes the relationship between the lines with the equations {{{ 9x-2y=5}}} and {{{-9x+9y=9}}}?

[A] parallel 
[B] perpendicular 
[C] neither parallel nor perpendicular 
[D] same line 

to find out, we need a slope;as you know, two lines  
that have {{{same}}} slope are {{{parallel}}},and do not intercept, there is no solution   
two lines  that have  slope negative reciprocal to each other are {{{perpendicular}}}

where the lines lie on top of each other, one equation can be rearranged to be the other equation precisely; this means when solving, you would get {{{y=y}}} and {{{x=x}}}, there are infinite solutions in this case (every point along the line would be a solution)

{{{ 9x-2y=5}}} and {{{-9x+9y=9}}}?
so, first write both equations in a slope-intercept form

{{{9x-2y=5}}}
 
{{{9x-5=2y}}}

{{{y=(9/2)x-5/5}}}

{{{y=(9/2)x-1}}}=> a slope is {{{(9/2)}}} and y-intercept is {{{-1}}}


and 

{{{-9x+9y=9}}}....both sides divide by {{{9}}}

{{{-x+y=1}}}

{{{y=x+1}}}=> a slope is {{{1}}} and y-intercept is {{{1}}}

So, both the lines have different slopes and different y- intercept which means the lines  neither parallel nor perpendicular 


{{{ graph( 600, 600, -10, 10, -10, 10,x+1, (9/2)x-1) }}}



that all  leads us  to the conclusion that your answer is: [C]