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

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

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

Start with the given system of equations:

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.

the distance between them is ; from the of first line to of second line
the of first line is
.......=>...........=>......
the point is (,)
the of second line is
.......=>...........=>......
the point is (,)

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:

Thus in our case, the required distance is

For more on this concept, refer to Distance formula.

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