Question 118671
An equation that is parallel has the same slope. So the slope of this parallel line is {{{m=-1/3}}}. Now just replace the 2 with any number such as 5 to get: {{{y=(-1/3)x+5}}}


So one parallel line is {{{y=(-1/3)x+5}}}



Notice if we graph the two equations, we can see that they are parallel. So this verifies our answer.



{{{ graph( 500, 500, -10, 10, -10, 10, (-1/3)x+2,(-1/3)x+5) }}} Graph of {{{y=(-1/3)x+2}}} (red) and {{{y=(-1/3)x+5}}} (green)




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An equation that is perpendicular has an negated inverted slope. Since the original slope is {{{m=-1/3}}}, the perpendicular slope is {{{-1/m=-1/(-1/3)=(-1/1)*(-3/1)=3/1=3}}}


So the perpendicular slope is {{{m=3}}}


{{{y=3x+2}}} Now just replace the slope of  {{{m=-1/3}}} with the new slope {{{m=3}}} to get a perpendicular line.



So one perpendicular line is {{{y=3x+2}}}




Notice if we graph the two equations, we can see that they are perpendicular. So this verifies our answer.



{{{ graph( 500, 500, -10, 10, -10, 10, (-1/3)x+2,3x+2) }}} Graph of {{{y=(-1/3)x+2}}} (red) and {{{y=3x+2}}} (green)