Question 408915
{{{y = (-1/3)x – 5}}}...this is the slope-intercept form and we can say that slope {{{m=(-1/3)}} and y-intercept is {{{-5}}}


{{{-18x + 6y = 21}}}...write this equation in the slope-intercept form too

{{{6y =18x + 21}}}

{{{6y/6 =18x/6 + 21/6}}}

{{{y =3x + 3.5}}}.........we can say that slope {{{m=3}} and y-intercept is {{{3.5}}}

so the slopes of our lines are {{{m=(-1/3)}} and {{{m=3}}

If {{{2}}} lines are {{{parallel}}} they have the {{{same}}} slope; evidently, these two lines are {{{not}}} {{{parallel}}}.

If they are {{{perpendicular}}}, their slopes {{{multiply}}} to get {{{-1}}}; 

so {{{m1 = -1/m2}}}

let's check it:

{{{-1/3 = -1/3}}}.........they are {{{perpendicular}}}

let's see their graph:


{{{ graph( 500, 500, -10, 10, -10, 10, 3x+3.5, -0.33x-5) }}}