SOLUTION: Write an equation that is parrallel and perpendicular to the given line. y=-1/3x+2

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Question 118671: Write an equation that is parrallel and perpendicular to the given line.
y=-1/3x+2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
An equation that is parallel has the same slope. So the slope of this parallel line is m=-1%2F3. Now just replace the 2 with any number such as 5 to get: y=%28-1%2F3%29x%2B5

So one parallel line is y=%28-1%2F3%29x%2B5


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


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C%28-1%2F3%29x%2B5%29+ Graph of y=%28-1%2F3%29x%2B2 (red) and y=%28-1%2F3%29x%2B5 (green)



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An equation that is perpendicular has an negated inverted slope. Since the original slope is m=-1%2F3, the perpendicular slope is -1%2Fm=-1%2F%28-1%2F3%29=%28-1%2F1%29%2A%28-3%2F1%29=3%2F1=3

So the perpendicular slope is m=3

y=3x%2B2 Now just replace the slope of m=-1%2F3 with the new slope m=3 to get a perpendicular line.


So one perpendicular line is y=3x%2B2



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


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C3x%2B2%29+ Graph of y=%28-1%2F3%29x%2B2 (red) and y=3x%2B2 (green)