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

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Question 118415: Write an equation that is parrallel and perpendicular to the given line.
y=-1/3x+2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Given line:
y=-%281%2F3%29x%2B2…… point-slope formula where slope m is -1%2F3

Parallel lines have equal+slopes; m%5B1%5D+=+m%5B2%5D.
Perpendicular+lines have slopes whose product is -1; m%5B1%5D+%2A+m%5B2%5D=+-1.
1) You need a line with slope -1%2F3
So, le say that line is:
y=-%281%2F3%29x+-+5…… point-slope formula of +parallel+line
%281%2F3%29x+%2B+y+=+-5…… standard formula of +parallel+line

here is the graph:

Solved by pluggable solver: Solve the System of Equations by Graphing


Let's look at the first equation %281%2F3%29x%2By=2



3%28%281%2F3%29x%2By%29=3%282%29 Multiply both sides of the first equation by the LCD 3



1x%2B3y=6 Distribute



---------



Let's look at the second equation %281%2F3%29x%2By=-5


3%28%281%2F3%29x%2By%29=3%28-5%29 Multiply both sides of the second equation by the LCD 3



1x%2B3y=-15 Distribute



---------




So our new system of equations is:


1x%2B3y=6

1x%2B3y=-15





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


1x%2B3y=6 Start with the given equation



3y=6-x Subtract +x from both sides



3y=-x%2B6 Rearrange the equation



y=%28-x%2B6%29%2F%283%29 Divide both sides by 3



y=%28-1%2F3%29x%2B%286%29%2F%283%29 Break up the fraction



y=%28-1%2F3%29x%2B2 Reduce



Now lets graph y=%28-1%2F3%29x%2B2 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%29+ Graph of y=%28-1%2F3%29x%2B2




So let's solve for y on the second equation


1x%2B3y=-15 Start with the given equation



3y=-15-x Subtract +x from both sides



3y=-x-15 Rearrange the equation



y=%28-x-15%29%2F%283%29 Divide both sides by 3



y=%28-1%2F3%29x%2B%28-15%29%2F%283%29 Break up the fraction



y=%28-1%2F3%29x-5 Reduce





Now lets add the graph of y=%28-1%2F3%29x-5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C%28-1%2F3%29x-5%29+ Graph of y=%28-1%2F3%29x%2B2(red) and y=%28-1%2F3%29x-5(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.





2) You need a line with slope %281%2F3%29%2A+m%5B2%5D=+-1
+m%5B2%5D=+-%281%2F%281%2F3%29%29
+m%5B2%5D=+-3
So, le say that line is:
y=+-3x+-+5…… point-slope formula of perpendicular+line
-3x+%2B+y+=+-5…… standard formula of perpendicular+line

here is the graph:

Solved by pluggable solver: Solve the System of Equations by Graphing


Let's look at the first equation %281%2F3%29x%2By=2



3%28%281%2F3%29x%2By%29=3%282%29 Multiply both sides of the first equation by the LCD 3



1x%2B3y=6 Distribute



---------




So our new system of equations is:


1x%2B3y=6

-3x%2By=-5





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


1x%2B3y=6 Start with the given equation



3y=6-x Subtract +x from both sides



3y=-x%2B6 Rearrange the equation



y=%28-x%2B6%29%2F%283%29 Divide both sides by 3



y=%28-1%2F3%29x%2B%286%29%2F%283%29 Break up the fraction



y=%28-1%2F3%29x%2B2 Reduce



Now lets graph y=%28-1%2F3%29x%2B2 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%29+ Graph of y=%28-1%2F3%29x%2B2




So let's solve for y on the second equation


-3x%2By=-5 Start with the given equation



1y=-5%2B3x Add 3+x to both sides



1y=%2B3x-5 Rearrange the equation



y=%28%2B3x-5%29%2F%281%29 Divide both sides by 1



y=%28%2B3%2F1%29x%2B%28-5%29%2F%281%29 Break up the fraction



y=3x-5 Reduce





Now lets add the graph of y=3x-5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%2B2%2C3x-5%29+ Graph of y=%28-1%2F3%29x%2B2(red) and y=3x-5(green)


From the graph, we can see that the two lines intersect at the point (21%2F10,13%2F10) (note: you might have to adjust the window to see the intersection)