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

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Question 118414: Write an equation that is parrallel and perpendicular to the given line.
y=2x-2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that parallel lins have equal+slopes;
m%5B1%5D+=+m%5B2%5D
Since given y=2x-2 which is slope-intercept form…=>… slope m%5B1%5D=+2
It will be also slope of the line parallel to given line
Let use this line y=2x%2B5
Here is the graph of both lines showing they are parallel:

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



Start with the given system of equations:


2x-y=2

2x-y=-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


2x-y=2 Start with the given equation



-y=2-2x Subtract 2+x from both sides



-y=-2x%2B2 Rearrange the equation



y=%28-2x%2B2%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%282%29%2F%28-1%29 Break up the fraction



y=2x-2 Reduce



Now lets graph y=2x-2 (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+2x-2%29+ Graph of y=2x-2




So let's solve for y on the second equation


2x-y=-5 Start with the given equation



-y=-5-2x Subtract 2+x from both sides



-y=-2x-5 Rearrange the equation



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



y=%28-2%2F-1%29x%2B%28-5%29%2F%28-1%29 Break up the fraction



y=2x%2B5 Reduce





Now lets add the graph of y=2x%2B5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-2%2C2x%2B5%29+ Graph of y=2x-2(red) and y=2x%2B5(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.



when lines are perpendicular slopes are negative reciprocals, so
m%5B2%5D+=+-1%2Fm%5B1%5D
m%5B2%5D+=+-1%2F2
Let use this line:
y+=+-%281%2F2%29x+

Here is the graph of both lines showing they are perpendicular:

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



Start with the given system of equations:


2x-y=2

-05x-y=0





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


2x-y=2 Start with the given equation



-y=2-2x Subtract 2+x from both sides



-y=-2x%2B2 Rearrange the equation



y=%28-2x%2B2%29%2F%28-1%29 Divide both sides by -1



y=%28-2%2F-1%29x%2B%282%29%2F%28-1%29 Break up the fraction



y=2x-2 Reduce



Now lets graph y=2x-2 (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+2x-2%29+ Graph of y=2x-2




So let's solve for y on the second equation


-05x-y=0 Start with the given equation



-y=0%2B05x Add 05+x to both sides



-y=%2B05x%2B0 Rearrange the equation



y=%28%2B05x%2B0%29%2F%28-1%29 Divide both sides by -1



y=%28%2B05%2F-1%29x%2B%280%29%2F%28-1%29 Break up the fraction



y=-5x%2B0 Reduce





Now lets add the graph of y=-5x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x-2%2C-5x%2B0%29+ Graph of y=2x-2(red) and y=-5x%2B0(green)


From the graph, we can see that the two lines intersect at the point (2%2F7,-10%2F7) (note: you might have to adjust the window to see the intersection)