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(20850)   (Show Source): You can put this solution on YOUR website!

Given line:
…… point-slope formula where slope is

lines have ; .
lines have slopes whose product is ; .
1) You need a line with slope
So, le say that line is:
…… point-slope formula of line
…… standard formula of line

here is the graph:

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


Let's look at the first equation



Multiply both sides of the first equation by the LCD 3



Distribute



---------



Let's look at the second equation


Multiply both sides of the second equation by the LCD 3



Distribute



---------




So our new system of equations is:










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


Start with the given equation



Subtract from both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce



Now lets graph (note: if you need help with graphing, check out this solver)



Graph of




So let's solve for y on the second equation


Start with the given equation



Subtract from both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce





Now lets add the graph of to our first plot to get:


Graph of (red) and (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


So, le say that line is:
…… point-slope formula of line
…… standard formula of line

here is the graph:

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


Let's look at the first equation



Multiply both sides of the first equation by the LCD 3



Distribute



---------




So our new system of equations is:










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


Start with the given equation



Subtract from both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce



Now lets graph (note: if you need help with graphing, check out this solver)



Graph of




So let's solve for y on the second equation


Start with the given equation



Add to both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce





Now lets add the graph of to our first plot to get:


Graph of (red) and (green)


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