Question 916314
{{{y = 5x -12}}} and {{{y-5x = 19}}}


Are the lines parallel, perpendicular, or neither?

if they have same slopes, they will be parallel
if their slopes are negative reciprocals, they will be perpendicular
if not neither of above, then lines neither parallel nor perpendicular

check if they have same slopes:
{{{y = highlight(5)x -12}}} ...slope is {{{5}}}

{{{y -5x = 19}}}=>{{{y = highlight(5)x+ 19}}}...slope is {{{5}}}

as you can see, they have same slope; so, your lines are {{{parallel}}}


graph them:

since you have linear functions, graph will be a line and you need only two points to graph each line


easiest is to find {{{x}}} and {{{y-intercept}}}

{{{y = 5x-12}}} ...set {{{y=0}}}

{{{0 = 5x -12}}}

{{{12= 5x }}}

{{{12/5= x }}}

{{{2.4= x }}}

x-intercept is at ({{{ 2.4}}}, {{{ 0 }}})


{{{y = 5x -12}}} ...set {{{x=0}}}

{{{y = 5*0 -12}}}

{{{y= -12}}}


y-intercept is at ({{{ 0 }}}, {{{ -12 }}})


now {{{y -5x = 19}}}

{{{y -5x = 19}}} ...set {{{y=0}}}

{{{0 -5x = 19}}} 

{{{-5x = 19}}} 

{{{x = 19/-5}}}
 
{{{x = -3.8}}} 

x-intercept is at ({{{ -3.8 }}}, {{{ 0 }}})


{{{y -5x = 19}}} ...set {{{x=0}}}

{{{y -5*0 = 19}}}

{{{y=19}}}


y-intercept is at ({{{ 0 }}}, {{{ 19 }}})


plot these points and draw a graphs:


{{{ graph( 600, 600, -25, 20, -20, 30, 5x+19, 5x -12) }}}