SOLUTION: Graph the lines and calculate the distance between them. y=-2x+5 and y=-2x-5

Algebra ->  Graphs -> SOLUTION: Graph the lines and calculate the distance between them. y=-2x+5 and y=-2x-5      Log On


   

Question 699935: Graph the lines and calculate the distance between them.
y=-2x+5 and y=-2x-5
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y=-2x%2B5
y=-2x-5

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



Start with the given system of equations:


2x%2By=5

2x%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


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



1y=5-2x Subtract 2+x from both sides



1y=-2x%2B5 Rearrange the equation



y=%28-2x%2B5%29%2F%281%29 Divide both sides by 1



y=%28-2%2F1%29x%2B%285%29%2F%281%29 Break up the fraction



y=-2x%2B5 Reduce



Now lets graph y=-2x%2B5 (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%2B5%29+ Graph of y=-2x%2B5




So let's solve for y on the second equation


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



1y=-5-2x Subtract 2+x from both sides



1y=-2x-5 Rearrange the equation



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



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



y=-2x-5 Reduce





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


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B5%2C-2x-5%29+ Graph of y=-2x%2B5(red) and y=-2x-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.



the distance between them is 5; from the x-intercept of first line to x-intercept of second line
the x-intercept of first line is
0=-2x%2B5.......=>......2x=5.....=>......x=5%2F2=2.5
the x-intercept point is (2.5,0)
the x-intercept of second line is
0=-2x-5.......=>......2x=-5.....=>......x=-5%2F2=-2.5
the x-intercept point is (-2.5,0)

the distance between these two points is the distance between two given lines:

Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%282.5--2.5%29%5E2+%2B+%280-0%29%5E2%29=+5+


For more on this concept, refer to Distance formula.